Exhibit 10.4

SCIENTIFIC ADVISOR AGREEMENT

THIS SCIENTIFIC ADVISOR AGREEMENT (this “Agreement”) is made and entered into as of December 31, 2015 (the “Effective Date”), by and among Zosano Pharma Corporation, a Delaware corporation having its principal place of business at 34790 Ardentech Court, Fremont, California 94555 (the “Parent”), ZP Opco, Inc., a Delaware corporation and wholly owned subsidiary of Parent (the “Company”), and PETER DADDONA, an individual residing at 35 Anderson Way, Menlo Park, California 94025 (the “Advisor”). The Parent, Company and Advisor may be referred to herein individually as a “Party” or collectively as the “Parties.”

Recitals

WHEREAS, the Advisor is currently a director of the Parent, an employee of the Company and the Chief Scientific Officer of both the Parent and the Company;

WHEREAS, the Advisor desires (i) to resign as an employee of the Company and as an officer of the Parent and the Company, effective as of the Effective Date; and (ii) commencing on January 1, 2016, to provide scientific advisory services to the Company subject to the term and conditions set forth herein;

WHEREAS, the Company desires to retain Advisor to provide scientific advisory services subject to the terms and conditions set forth herein;

WHEREAS, the Advisor desires to continue to serve as a director of the Parent in accordance with the bylaws of the Parent;

NOW THEREFORE, in consideration of the foregoing premises and the mutual covenants set forth below, the Parties hereby agree as follows:

1. Scientific Advisory Services.

1.1 As further provided in Section 9.2, effective as of the Effective Date, the Advisor hereby resigns as an employee and officer of the Company and as an officer of the Parent.

1.2 Commencing on January 1, 2016 (the “Start Date”), the Company hereby retains Advisor, and Advisor hereby agrees to perform such scientific advisory services for the Company as set forth in Section 1 of Exhibit A (collectively, the “Services”). Advisor shall report to the Parent’s Chief Executive Officer or, if requested to do so by the Chief Executive Officer, report to the Parent’s Chief Scientific Officer. The specific nature and amount of the Services shall be as determined by the Company during the term of this Agreement; provided, however, that Advisor agrees that during the Term (as defined in Section 9.1 below), Advisor shall be available to provide Services, either in person or via telephone at the Company’s discretion, on two days of each month, subject to reasonable advance notice by the Company, for four hours on each day (for a total of eight hours per month). Advisor agrees to perform the Services, and provide the results thereof, with the highest degree of professional skill and expertise. Advisor may use the assistance of other individuals who are not employees of the Company only with the prior written consent of the Company.

1.3 For the avoidance of doubt, the Advisor acknowledges that he is currently a director of the Parent and will continue to serve as a director of the Parent, in accordance with the Parent’s bylaws, until the earliest of his death, resignation (as a director), or removal. Advisor acknowledges that he will not qualify as an “independent director” within the meaning of NASDAQ listing rule 5605(a)(2) and will not be eligible for any of the compensation that the Parent pays to its independent directors.

2. Compensation.

Section 2 of Exhibit A attached hereto sets forth the amount and timing of payment for the Services and reimbursable expenses. The Company will reimburse Advisor for expenses actually incurred by Advisor in performing the Services, including but not limited to travel and accommodation expenses, so long as such expenses are reasonable and necessary as determined by the Company and approved in advance by Company. Advisor shall maintain adequate books and records relating to any expenses to be reimbursed and shall submit requests for reimbursement in a timely manner and form acceptable to the Company.

3. Independent Contractor.

The Parties understand and agree that Advisor is an independent contractor and not an agent or employee of the Company. Advisor has no authority to obligate the Company by contract or otherwise. Advisor will not be eligible for any employee benefits, nor will the Company make deductions from Advisor’s fees for taxes or insurance (except as otherwise required by applicable law or regulation). Any payroll and employment taxes, insurance, and benefits imposed on Advisor due to activities performed hereunder will be the sole responsibility of Advisor.

4. Recognition of Company’s Rights; Nondisclosure.

Advisor recognizes that the Company is engaged in a continuous program of research and development respecting its present and future business activities. Advisor agrees as follows:

4.1 At all times during the term of Advisor’s association with the Company and thereafter, Advisor will hold in strictest confidence and will not disclose, use, lecture upon or publish any of the Company’s Proprietary Information (defined below), except to the extent such disclosure, use or publication may be required in direct connection with Advisor’s performing requested Services for the Company or is expressly authorized in writing by an officer of the Company. It is understood that the Proprietary Information will remain the sole property of the Company. Advisor further agrees to take all reasonable precautions to prevent any unauthorized disclosure of the Proprietary Information including, but not limited to, having each employee, agent or representative of Advisor, if any, with access to any Proprietary Information execute a nondisclosure agreement containing provisions in the Company’s favor substantially similar to Sections 4 and 13 of this Agreement.

4.2 The term “Proprietary Information” shall mean any and all trade secrets, confidential knowledge, know-how, data or other proprietary information or materials of the Company, the Parent or any of their respective affiliates. By way of illustration but not limitation, Proprietary Information includes: (i) inventions, ideas, samples, prototypes, devices, hardware, software, electronic components and materials, and procedures for producing any such

items, as well as data, know-how, improvements, inventions, discoveries, developments, designs and techniques; (ii) information regarding plans for research, development, new products, marketing and selling activities, business models, budgets and unpublished financial statements, licenses, prices and costs, suppliers and customers; and (iii) information regarding the skills and compensation of employees or consultants of the Company.

4.3 In addition, Advisor understands that the Company has received and in the future will receive from third parties confidential or proprietary information (“Third Party Information”) subject to a duty on the Company’s part to maintain the confidentiality of such information and to use it only for certain limited purposes. During the term of Advisor’s association with the Company and thereafter, Advisor will hold Third Party Information in the strictest confidence and will not disclose or use Third Party Information, except in connection with Advisor’s performing requested Services for the Company, or as expressly authorized in writing by an officer of the Company.

5. Intellectual Property Rights.

5.1 Advisor shall promptly and fully disclose to the Company any and all ideas, inventions, technologies, discoveries, improvements, know-how and techniques that the Advisor conceives, reduces to practice or develops during the term of this Agreement, alone or in conjunction with others, and in any way related to or arising from (i) the Company’s Field (as defined in Section 6.1), (ii) the Services, or (iii) Proprietary Information (collectively, the “Inventions”). Advisor agrees to keep and maintain adequate and current records (in the form of notes, sketches, drawings or in any other form that may be required by the Company) of all Services provided and results thereof and such records shall be available to and remain the sole property of the Company at all times. Advisor agrees that any and all Inventions, including any related patents, copyrights, trade secrets and trademark rights, shall be the sole and exclusive property of the Company.

5.2 Advisor hereby assigns to the Company his entire right, title and interest in and to all Inventions. Advisor hereby designates the Company as his agent for, and grants to the Company a power of attorney, which power of attorney shall be deemed coupled with an interest, solely for the purpose of effecting the foregoing assignment from the Advisor to the Company. Advisor will perform other activities necessary to effect the intent of this Section 5.2.

5.3 Advisor further agrees to cooperate and provide reasonable assistance to the Company to obtain and from time to time enforce United States and foreign patents, copyrights, and other rights and protections claiming, covering or relating to the Inventions in any and all countries.

5.4 Advisor agrees to submit to the Company any proposed publication that contains any discussion relating to the Company, Proprietary Information, Inventions or work performed by Advisor for the Company hereunder. Advisor further agrees that no such publication shall be made without the prior written consent of the Company, which consent shall not be unreasonably withheld.

6. Noncompetition and Nonsolicitation of Employees.

6.1 During the term of this Agreement, Advisor will not, without the prior consent of the Company’s Board of Directors, engage in any commercial business activity that competes in any way with any business then being conducted or planned by the Company relating to the research, discovery, development, manufacture or commercialization of transdermal drug delivery systems or patches for administering pharmaceutical compounds to humans (the “Company’s Field”).

6.2 During the term of this Agreement and for one (1) year after its termination, Advisor will not personally or through others recruit, solicit or induce any employee of the Company to terminate his or her employment with the Company.

6.3 If any restriction set forth in Sections 6.1 and 6.2 is found by any court of competent jurisdiction to be unenforceable because it extends for too long a period of time or over too great a range of activities or in too broad a geographic area, it shall be interpreted to extend only over the maximum period of time, range of activities or geographic area as to which it may be enforceable.

7. No Conflicting Obligation.

7.1 Advisor represents that Advisor’s performance of all of the terms of this Agreement and the performing of the Services for the Company do not and will not breach or conflict with any agreement with a third party, including an agreement to keep in confidence any proprietary information of another entity acquired by Advisor in confidence or in trust prior to the date of this Agreement.

7.2 Advisor hereby agrees not to enter into any agreement that conflicts with this Agreement.

8. No Improper Use of Materials.

Advisor agrees not to bring to the Company or to use in the performance of Services for the Company any materials or documents of a present or former employer of Advisor, or any materials or documents obtained by Advisor from a third party under a binder of confidentiality, unless such materials or documents are generally available to the public or Advisor has authorization from such present or former employer or third party for the possession and unrestricted use of such materials. Advisor understands that Advisor is not to breach any obligation of confidentiality that Advisor has to present or former employers or clients, and agrees to fulfill all such obligations during the term of this Agreement.

9. Term and Termination.

9.1 Advisor’s Services under this Agreement shall commence on the Effective Date and shall continue for a term of one (1) year from and after the Effective Date (the “Term”), unless earlier terminated as provided below in this Section 9. Unless earlier terminated as provided below in this Section 9 or otherwise agreed upon in writing by the Company and Advisor, this Agreement shall automatically terminate upon the expiration of the Term (which, for the avoidance of doubt, is January 1, 2017).

9.2 Effective December 31, 2015 (the “Resignation Date”), Advisor hereby resigns from his position as Chief Scientific Officer of the Company and Parent and from any

other positions (excluding director) Advisor may currently hold as a fiduciary of the Company or of Parent. Advisor and the Company hereby acknowledge and agree that the Resignation Date is the effective date of termination of Advisor’s employment with the Company and its affiliates, and that such resignation is a voluntary termination of employment by Advisor other than for Good Reason pursuant to the last sentence of Section 4(b) of that certain employment letter agreement dated May 11, 2012 among the Company and Advisor, as amended by the letter amendments thereto dated January 6, 2014, January 16, 2014 and May 29, 2015 (as so amended, the “Employment Agreement”). In connection with Advisor’s voluntary termination of employment, (i) the Company (x) hereby waives the thirty (30)-day written notice period described in the last sentence of Section 4(b) of the Employment Agreement and (y) acknowledges its obligations under Section 5(d) of the Employment Agreement to pay Advisor his accrued but unpaid base salary and any accrued but unpaid vacation time, in each case earned by Advisor while an employee of the Company through the Resignation Date (less applicable taxes and withholding); and (ii) Advisor acknowledges that the Company shall have no obligation to Advisor for any severance payments under the Employment Agreement and, except for any right Advisor may have under the federal law known as “COBRA” to continue participation in the Company’s group health and dental plans at Advisor’s cost, Advisor’s benefits shall terminate in accordance with the terms of the applicable benefit plans. In addition, Advisor acknowledges (i) his obligation, in accordance with Section 5(f) of the Employment Agreement, to continue to fully perform following the Resignation Date Advisor’s obligations under Section 3 of the Employment Agreement and (ii) that the Advisor’s Incentive Stock Option dated June 15, 2012 between the Company and Advisor (the “2012 Option”) will lose its status as an incentive stock option 90 days’ after the Resignation Date and will be treated as a non-qualified stock option from that point forward. For the avoidance of doubt, the 2012 Option will continue to vest pursuant to the vesting schedule described therein for so long as the Advisor continues to provide Services to the Company or Parent pursuant to this Agreement.

9.3 Either Party may terminate this Agreement for any reason upon 30 days’ written notice provided to the other Party.

9.4 The Company will amend the 2012 Option to provide as follows:

(a) In the event that the Advisor provides Services for the entire Term then Advisor may exercise the 2012 Option at any time prior to December 31, 2017;

(b) In the event that Company terminates this Agreement without cause (e.g., no breach by Advisor) prior to the expiration of the Term then Advisor may exercise the 2012 Option at any time prior to the first anniversary of the date of termination; and

(c) In the event that Advisor terminates the Agreement, or if the Company terminates it for cause (e.g., breach by Advisor), prior to the expiration of the Term then Advisor may exercise the 2012 Option at any time within 90 days after the date of termination.

9.5 The obligations set forth in Sections 4, 5, 6 and 9 through 16 will survive any termination or expiration of this Agreement. Upon termination of this Agreement, Advisor will cease work immediately after giving or receiving such notice of termination, unless otherwise advised by the Company, and promptly deliver to the Company all documents and other materials of any nature pertaining to the Services, together with all documents and other items containing or pertaining to any Proprietary Information.

10. Assignment.

The rights and liabilities of the Parties hereto shall bind and inure to the benefit of their respective successors, heirs, executors and administrators, as the case may be; provided that, as the Company has specifically contracted for Advisor’s Services, Advisor may not assign or delegate Advisor’s obligations under this Agreement either in whole or in part without the prior written consent of the Company. The Company may assign its rights and obligations hereunder to any person or entity that succeeds to all or substantially all of the Company’s business. Any assignment not in accordance with this Section 10 shall be void.

11. Legal and Equitable Remedies.

Because Advisor’s Services are personal and unique and because Advisor may have access to and become acquainted with the Proprietary Information of the Company, the Company shall have the right to enforce this Agreement and any of its provisions by injunction, specific performance or other equitable relief without prejudice to any other rights and remedies that the Company may have for a breach of this Agreement.

12. Compliance with Applicable Laws and Obligations.

Advisor will perform the Services in compliance with all applicable laws.

13. Governing Law; Severability.

This Agreement shall be governed by and construed according to the laws of the State of Delaware, without regards to conflicts of laws rules. If any provision of this Agreement is found by a court of competent jurisdiction to be unenforceable, that provision shall be severed and the remainder of this Agreement shall continue in full force and effect.

14. Complete Understanding; Modification.

This Agreement, including the Exhibits mentioned herein, and the Employment Agreement constitute the final, exclusive and complete understanding and agreement of the Parties hereto and supersede all prior understandings and agreements with respect to the subject matter hereof. Any waiver, modification or amendment of any provision of this Agreement shall be effective only if in writing and signed by the Parties hereto.

15. Notices.

Any notices required or permitted hereunder shall be given to the appropriate Party at the address listed on the first page of this Agreement, or such other address as the Party shall specify in writing pursuant to this notice provision. Such notice shall be deemed given upon personal delivery to the appropriate address or three days after the date of mailing if sent by certified or registered mail.

16. Counterparts.

This Agreement may be executed in one or more counterparts each of which will be deemed an original, but all of which together shall constitute one and the same instrument.

IN WITNESS WHEREOF, the Parties hereto have executed this Scientific Advisor Agreement as of the date first written above.

EXHIBIT A

SCOPE AND COMPENSATION

1. Services: Advisor shall perform scientific advisory services as requested by the Company, including without limitation:

2. Consideration:

(a) Subject to Section 2(b), the Company will compensate Advisor at the rate of $4,000 per month for all Services performed and invoiced under this Agreement. On a monthly basis, Advisor shall submit to the Company a written invoice for services performed under this Agreement, which lists the dates that such services were performed. The Company will pay such invoices promptly following receipt, subject to the approval of an authorized representative of the Company.

(b) In the event that (i) the Company requests that the Consultant travel on its behalf (e.g., to attend a meeting with the FDA), (ii) the Consultant agrees to the request, and (iii) the trip causes him to provide more than eight hours of Services in a given month, then the Company shall pay him at a rate $500 per hour for each such excess hour, subject to a maximum fee of $2,500 day (plus reimbursement of expenses, as provided below).

3. Expenses that will be reimbursed: The Company shall reimburse Advisor for business expenses that are reasonable and necessary for Advisor to perform, and were incurred by Advisor in the course of the performance of Advisor’s duties pursuant to this Agreement and in accordance with the Company’s general policies. Such expenses shall be reimbursed upon Advisor’s submission of vouchers and an expense report in such form as may be required by the Company consistent with the Company’s policies in place from time-to-time.