Exhibit 1.1

AGREEMENT TO CONVERT

THIS AGREEMENT TO CONVERT (this “Agreement”) is entered into as of the 25th day of August, 2010, by and among Intervest Bancshares Corporation, a Delaware corporation (the “Company”), and Lowell S. Dansker, Jean Dansker and Helene Bergman (collectively, the “Class B Shareholders”).

WHEREAS, the Company is currently conducting a registered offering of shares of its Class A common stock, par value $1.00 per share (the “Class A Stock”), pursuant to a Registration Statement on Form S-1, SEC file number 333-167911 (the “Registration Statement”);

WHEREAS, each of the Class B Shareholders holds shares of the Class B common stock, par value $1.00 per share, of the Company (the “Class B Stock”), in the amount set forth opposite such person’s name in Appendix A hereto;

WHEREAS, in accordance with the Certificate of Incorporation of the Company, the shares of Class B Stock are convertible, at any time at the option of the holder thereof, into shares of Class A Stock, at the rate of one share of Class A Stock for one share of Class B Stock;

WHEREAS, without being solicited or being made aware of their conversion rights by the prospectus included in the Registration Statement, each of the Class B Shareholders desires, upon and contemporaneously with the closing of an offering of shares of the Company’s Class A common stock resulting in minimum gross proceeds to the Company of not less than $26,000,000 (the “Offering”), to convert his or her shares of Class B Stock into Class A Stock, upon the terms and conditions set forth in this Agreement;

NOW, THEREFORE, in consideration of the foregoing and the mutual covenants contained herein, the parties to this Agreement agree as follows:

1. Conversion. Subject to the terms and conditions of this Agreement, each of the Class B Shareholders hereby agrees to deposit with the Company all shares of Class B Stock held by them, the total number of which is set forth opposite such person’s name on Appendix A hereto for conversion into the number of shares of Class A Stock set forth opposite such person’s name on Appendix A hereto, together with such instruments of transfer as the Company may reasonably request. Each Class B Shareholder and the Company agree that the shares of Class B Stock so deposited shall be deemed to be delivered to the Company, and such conversion shall be effective, contingent upon and subject to the closing of the Offering.

2. Issuance of Certificates. Each Class B Shareholder requests that a certificate representing the shares of Class A Stock to be issued to such person pursuant to Section 1 above be issued to such Class B Shareholder, in the name of such Class B Shareholder as it appears on Appendix A hereto. Each Class B Shareholder acknowledges and agrees that the shares of Class A Stock issued to them have not been registered under the Securities Act of 1933 or any other securities or blue sky laws, may be sold or disposed of only pursuant to such laws, and that each certificate representing shares of Class A Stock issued to such Class B Shareholder shall bear legends restricting the transferability of shares of Class A Stock, no less restrictive than those on the certificates of Class B Stock so converted and surrendered in exchange therefor and that the Company’s transfer agent has been informed of such restrictions.

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3. Representations. Each Class B Shareholder hereby represents and warrants to the Company that: (a) he or she is the lawful owner of record and beneficially of all of the Class B Stock set forth opposite such person’s name on Appendix A hereto, free and clear of all pledges, liens, encumbrances, claims, security interests and other charges of any nature whatsoever; (b) he or she has the full legal power, authority and capacity required by law to surrender and deliver to the Company the shares of Class B Stock owned by him or her in accordance with this Agreement free and clear of all pledges, liens, encumbrances, claims, security interests and other charges of any nature whatsoever; and (c) he or she is acquiring the shares of Class A Stock for his or her own account without a view toward the public distribution or resale thereof, and such Class B Shareholder has no agreement or arrangement to sell or otherwise distribute, transfer or dispose of the shares of Class A Stock issuable hereunder to any other person. Each Class B Shareholder acknowledges that such person has access to information concerning the Company and its Class A Stock (including without limitation access to the Registration Statement and all amendments and supplements thereto), and that such Class B Shareholder has had an opportunity to discuss with management of the Company any questions such person has regarding an investment in the Class A Stock. Each Class B Shareholder acknowledges that the Company has not made any representation or warranty, express or implied, as to the accuracy or completeness of any information regarding the Company furnished or made available to such Class B Shareholder, except as expressly set forth in this Agreement.

4. Conditions to Obligation of Class B Shareholders. Notwithstanding the foregoing, if the Company notifies the Class B Shareholders in writing that the Offering has been abandoned or otherwise terminated without a closing thereunder, this Agreement shall terminate and any obligation of the Class B Shareholders to deposit their shares of Class B Stock with the Company for conversion, and any obligation of the Company to issue shares of Class A Stock in exchange therefor, as provided in this Agreement shall cease.

5. Miscellaneous.

(a) Each of the parties hereto agrees to cooperate with the others, take such further action, and execute and deliver such further documents and instruments, as may be reasonably requested by the other party in order to carry out the terms and purposes of this Agreement.

(b) This Agreement may be amended only by a written agreement executed by all parties hereto.

(c) This Agreement shall be binding upon and inure to the benefit of the parties hereto and their respective successors and assigns. This Agreement shall create no rights of any nature in any person not a party hereto.

(d) This Agreement shall be governed and construed in accordance with the laws of the State of New York applicable to agreements made and to be performed entirely within such State and without regard to principles of conflict of laws, except to the extent that the conversion of the Class B Stock may be governed by the Delaware General Corporation Law.

(e) This Agreement sets forth the entire understanding of the parties hereto with respect to the subject matter hereof, and supersedes and replaces any and all prior agreements and understandings, whether written or oral, relating to the subject matter hereof.

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IN WITNESS WHEREOF, the parties hereto have duly executed this Agreement as of the date first above written.

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Appendix A