Exhibit 5.1

[Cooley Letterhead]

May 21, 2020

Geron Corporation
919 East Hillsdale Boulevard, Suite 250
Foster City, CA 94404

Ladies and Gentlemen:

We have acted as counsel to Geron Corporation, a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-3 (the “Registration Statement”) filed by the Company pursuant to Rule 462(b) promulgated under the Securities Act of 1933, as amended (the “Act”), relating to an aggregate of $37,435,660 of shares of common stock, par value $0.001 per share (the “Common Stock”), of the Company (the “Shares”) and warrants to purchase Common Stock (the “Warrants”), which may be issued under one or more warrant agreements, to be dated on or about the date of the first issuance of the Warrants thereunder, by and between a warrant agent to be selected by the Company (the “Warrant Agent”) and the Company, in the form filed as an exhibit to the Prior Registration Statement (as defined below) (the “Warrant Agreement”). The Registration Statement incorporates by reference the registration statement on Form S-3 (File No.333-225184), which was declared effective on July 12, 2018 (the “Prior Registration Statement”), including the prospectus which forms a part of the Prior Registration Statement (the “Base Prospectus”), which provides that it will be supplemented in the future by one or more prospectus supplements (each a “Prospectus Supplement”).

The Common Stock and the Warrants are collectively referred to as the “Securities”. The Securities 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 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 of all signatures, 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 by all persons other than the Company where authorization, execution and delivery are prerequisites to the effectiveness of such documents.

With respect to our opinion as to the Common Stock, we have assumed that, at the time of issuance and sale, a sufficient number of shares of Common Stock is authorized and reserved or available for issuance and that the consideration for the issuance and sale of the Shares is in an amount that is not less than the par value of the Common Stock.

With respect to our opinion as to the Warrants, we have also assumed that any Warrants offered under the Registration Statement, and the related Warrant Agreement are executed in the forms filed as exhibits to the Registration Statement or incorporated by reference therein. We have also assumed that (i) with respect to Common Stock issuable upon exercise of any Warrants, such Warrants constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with their terms, except as enforcement may be limited by applicable bankruptcy, insolvency, reorganization, arrangement, moratorium or other similar laws affecting creditors’ rights, and subject to general equity principles and to limitations on availability of equitable relief, including specific performance.

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

Geron Corporation
May 21, 2020
Page Two

Our opinion herein is expressed solely with respect to the General Corporation Law of the State of Delaware, and, as to the Warrants constituting valid and legally binding obligations of the Company, the laws of the State of New York. 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 and in reliance thereon, and subject to the qualifications herein stated, we are of the opinion that:

1. With respect to the Common Stock offered under the Registration Statement, provided that (i) the Base Prospectus and any and all Prospectus Supplement(s) required by applicable laws have been delivered and filed as required by such laws; (ii) the issuance of the Common Stock has been duly authorized by all necessary corporate action on the part of the Company; (iii) the issuance and sale of the Common Stock do not violate any applicable law, are in conformity with the Company’s then operative certificate of incorporation (the “Certificate of Incorporation”) and bylaws (the “Bylaws”), do not result in a default under or breach of any agreement or instrument binding upon the Company and comply with any applicable requirement or restriction imposed by any court or governmental body having jurisdiction over the Company; and (iv) the certificates, if any, for the Common Stock have been duly executed by the Company, countersigned by the transfer agent therefor and duly delivered to the purchasers thereof against payment therefor, then the Common Stock, when issued and sold as contemplated in the Registration Statement, the Base Prospectus and the related Prospectus Supplement(s), and in accordance with a duly authorized, executed and delivered purchase, underwriting or similar agreement, or upon exercise of any Warrants in accordance with their terms, will be validly issued, fully paid and non-assessable.

2. With respect to the Warrants issued under the Warrant Agreement and offered under the Registration Statement, provided that (i) any and all Prospectus Supplement(s) required by applicable laws have been delivered and filed as required by such laws; (ii) the Warrant Agreement has been duly authorized by the Company and the Warrant Agent by all necessary corporate action; (iii) the Warrant Agreement has been duly executed and delivered by the Company and the Warrant Agent; (iv) the issuance and terms of the Warrants have been duly authorized by the Company by all necessary corporate action; (v) the terms of the Warrants and of their issuance and sale have been duly established in conformity with the Warrant Agreement and as described in the Registration Statement, the Base Prospectus and the related Prospectus Supplement(s), so as not to violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company, so as to be in conformity with the Certificate of Incorporation and Bylaws, and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company; and (vi) the Warrants have been duly executed and delivered by the Company and authenticated by the Warrant Agent pursuant to the Warrant Agreement and delivered against payment therefor, then the Warrants, when issued and sold as contemplated in the Registration Statement, the Base Prospectus and the Prospectus Supplement(s) and in accordance with the Warrant Agreement and a duly authorized, executed and delivered purchase, underwriting or similar agreement, will be valid and legally binding obligations of the Company, enforceable against the Company in accordance with their terms, except as enforcement thereof may be limited by bankruptcy, insolvency, reorganization, moratorium or other similar laws relating to or affecting creditors’ rights generally, and by general equitable principles (regardless of whether such enforceability is considered in a proceeding at law or in equity).

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to reference to our firm under the caption “Legal Matters” in the Base Prospectus.

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

Geron Corporation
May 21, 2020
Page Three

Our opinion set forth above is limited to the matters expressly set forth in this letter, and no opinion is implied or may be inferred beyond the matters expressly stated. This opinion speaks only as to law and facts in effect or existing as of the date hereof, and we undertake no obligation or responsibility to update or supplement this opinion to reflect any facts or circumstances that may hereafter come to our attention or any changes in law that may hereafter occur.

Sincerely,

Cooley LLP

By:	/s/ Chadwick Mills
	CHADWICK L. MILLS

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