EXHIBIT 5.1

Chadwick L. Mills
+1 650 843 5654
cmills@cooley.com

May 18, 2018

Geron Corporation
149 Commonwealth Drive
Menlo Park, CA 94025

Ladies and Gentlemen:

We have acted as counsel to Geron Corporation, a Delaware corporation (the “Company”), with respect to certain matters in connection with the offering by the Company of up to $100,000,000 of the Company’s common stock, par value $0.001 (the “Shares”), pursuant to a Registration Statement on Form S-3 (No. 333-206659) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), the prospectus included within the Registration Statement (the “Base Prospectus”), and the prospectus supplement dated May 18, 2018, filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations of the Securities Act (the “Prospectus Supplement” and together with the Base Prospectus, the “Prospectus.”). The Shares are to be sold by the Company in accordance with an At-Market Issuance Sales Agreement, dated May 18, 2018, between the Company and B. Riley FBR, Inc. (the “Agreement”), as described in the Prospectus. The Shares are being registered for offer and sale from time to time pursuant to Rule 415 under the Securities Act.

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and the Prospectus, (b) the Company’s Certificate of Incorporation and Bylaws, each as currently in effect, and (c) originals, or copies certified to our satisfaction, of such records, documents, certificates, opinions, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters. In rendering this opinion, we have assumed the genuineness and authenticity of all signatures on original documents; the authenticity of all documents submitted to us as originals; the conformity to originals of all documents submitted to us as copies; the accuracy, completeness and authenticity of certificates of public officials; and the due authorization, execution and delivery of all documents where authorization, execution and delivery are prerequisites to the effectiveness of such documents.

We have assumed (i) that each sale of Shares will be duly authorized by the Board of Directors of the Company, a duly authorized committee thereof or a person or body pursuant to an authorization granted in accordance with Section 152 of the General Corporation Law of the State of Delaware (the DGCL”), (ii) that no more than 29,585,799 shares of common stock will be sold under the Agreement based on a sale price of $3.38 per share, representing the last reported sale price of the Common Stock on the NASDAQ Global Select Market on May 17, 2018 and (iii) that the price at which the Shares are sold will equal or exceed the par value of the Shares. We express no opinion to the extent that future issuances of securities of the Company and/or anti-dilution adjustments to outstanding securities of the Company cause the number of shares of the Company’s common stock outstanding or issuable upon conversion or exercise of outstanding securities of the Company to equal or exceed the number of Shares then issuable under the Agreement.

Cooley LLP    101 California Street    5th Floor    San Francisco, CA    94111-5800
t: (415) 693-2000   f: (415) 693-2222   cooley.com

May 18, 2018
Page Two

Our opinion herein is expressed solely with respect to the General Corporation Law of the State of Delaware. Our opinion is based on these laws as in effect on the date hereof. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing, we are of the opinion that the Shares, when issued and paid for in accordance with the Agreement and as provided in the Registration Statement and the Prospectus, the Shares will be validly issued, fully paid and nonassessable.

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We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to our firm under the caption “Legal Matters” in the Base Prospectus and the Prospectus Supplement included in the Registration Statement. This opinion is expressed as of the date hereof, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable law.

Sincerely,

Cooley LLP

Cooley LLP    101 California Street    5th Floor    San Francisco, CA    94111-5800
t: (415) 693-2000   f: (415) 693-2222   cooley.com