Exhibit 5.1

Chadwick L. Mills
(650) 843-5654
cmills@cooley.com

January 30, 2014

Geron Corporation
149 Commonwealth Drive
Menlo Park, California 94025

RE: Geron Corporation

Ladies and Gentlemen:

We have acted as counsel to Geron Corporation, a Delaware corporation (the “Company”) and you have requested our opinion with respect to certain matters in connection with the offering by the Company, of up to 25,875,000 shares (the “Shares”) (including up to 3,375,000 shares that may be sold pursuant to the exercise of an over-allotment option) of the Company’s common stock, par value $0.001 per share (the “Common Stock”), pursuant to a Registration Statement on Form S-3, as amended (Registration No. 333-182537) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), the related prospectus dated October 11, 2012 included in the Registration Statement (the “Base Prospectus”) and the prospectus supplement dated January 30, 2014, filed with the Commission pursuant to Rule 424(b) under the Act (the “Prospectus Supplement”). (The Base Prospectus and the Prospectus Supplement are collectively referred to as the “Prospectus.”) The Shares are to be sold by the Company as described in the Registration Statement and the Prospectus.

In connection with this opinion, we have examined and relied upon the Registration Statement and the Prospectus, the Company’s Certificate of Incorporation, as amended, and Bylaws, each as currently in effect, and the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. We have assumed the genuineness and authenticity of all documents submitted to us as originals, and the conformity to originals of all documents submitted to us as copies.

Our opinion is expressed only with respect to the federal laws of the United States of America and the General Corporation Law of the State of Delaware.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when sold in accordance with the Registration Statement and the Prospectus, will be validly issued, fully paid and nonassessable.

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus included in the Registration Statement and to the filing of this opinion as an exhibit to a current report of the Company on Form 8-K.

Very truly yours,

COOLEY LLP

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