Exhibit 5.1

Cooley

Sean M. Clayton

+1 858 550 6034

sclayton@cooley.com

February 28, 2018

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”), with respect to certain matters 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 an aggregate of up to 885,596 shares of the Company's Common Stock, $0.001 par value (the “Shares”), including 708,477 shares issuable pursuant to the Company’s 2015 Equity Incentive Plan (the “Incentive Plan”) and 177,119 shares issuable pursuant to the Company’s 2015 Employee Stock Purchase Plan (the “Employee Plan”).

In connection with this opinion, we have examined and relied upon the Registration Statement and related prospectuses, the Incentive Plan, the Employee Plan, the Company's Amended and Restated Certificate of Incorporation and Bylaws, 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 thereof.  Our opinion is expressed only with respect to 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 issued and sold in accordance with the Incentive Plan or the Employee Plan, as applicable, the Registration Statement and related prospectus, will be validly issued, fully paid and nonassessable (except as to shares issued pursuant to certain deferred payment arrangements under the Incentive Plan 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