Exhibit 5.1

Sean M. Clayton

+1 858 550 6034

sclayton@cooley.com

February 25, 2021

TRACON Pharmaceuticals, Inc.

4350 La Jolla Village Drive, Suite 800

San Diego, California 92122

Ladies and Gentlemen:

You have requested our opinion, as counsel to TRACON Pharmaceuticals, Inc., a Delaware corporation (the “Company”), in connection with the filing by the Company of a Registration Statement on Form S-8 (the “Registration Statement”) with the Securities and Exchange Commission covering the offering of up to 655,843 shares (the “Shares”) of the Company's Common Stock, par value $0.001 per share (“Common Stock”), including (i) 619,151 shares of Common Stock issuable pursuant to the Company’s 2015 Equity Incentive Plan (the “Incentive Plan”) and (ii) 36,692 shares of Common Stock issuable pursuant to the Company’s 2015 Employee Stock Purchase Plan (together with the Incentive Plan, the “Plans”).

In connection with this opinion, we have examined and relied upon the Registration Statement and related prospectuses, the Plans, the Company’s Certificate of Incorporation and Bylaws, each as currently in effect, and 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 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. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.  

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware. 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, we are of the opinion that the Shares, when sold and issued in accordance with the Plans, the Registration Statement and related prospectuses, will be validly issued, fully paid and nonassessable (except as to Shares issued pursuant to certain deferred payment arrangements, which will be fully paid and nonassessable when such deferred payments are made in full).

We consent to the filing of this opinion as an exhibit to the Registration Statement.

Sincerely,

Cooley LLP

By:  /s/ Sean M. Clayton

            Sean M. Clayton

4401 Eastgate Mall, San Diego, CA 92121  T: (858) 550-6000  F: (858) 550-6420  www.cooley.com