Exhibit 5.1

SEAN M. CLAYTON

+1 858 550 6034

sclayton@cooley.com

March 27, 2017

TRACON Pharmaceuticals, Inc.

8910 University Center Lane, Suite 700

San Diego, CA 92122

Ladies and Gentlemen:

You have requested our opinion with respect to certain matters in connection with the filing by TRACON Pharmaceuticals, Inc., a Delaware corporation (the “Company”), of a Registration Statement on Form S-1 (the “Registration Statement”) with the Securities and Exchange Commission, covering the registration for resale of (i) 417,948 shares (the “Shares”) of the Company’s common stock, par value $0.001, issued to Aspire Capital Fund, LLC (“Aspire”), and (ii) up to 2,813,567 shares of the Company’s common stock, par value $0.001 (the “Agreement Shares”) that may be issued from time to time pursuant to a common stock purchase agreement dated March 14, 2017 (the “Purchase Agreement”), between the Company and Aspire.

In connection with this opinion, we have examined and relied upon the Registration Statement and related prospectus, the Company’s Certificate of Incorporation, as amended, and its Amended and Restated Bylaws, each as currently in effect, the Purchase Agreement and the originals or copies certified to our satisfaction of such other 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, the conformity to originals of all documents submitted to us as copies thereof and the due execution and delivery of all documents where due execution and delivery are a prerequisite to the effectiveness thereof. As to certain factual matters, including without limitation the receipt by the Company of the purchase price for the Shares as provided in the Purchase Agreement, we have relied upon a certificate of an officer of the Company and have not sought independently to verify such matters.

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware. We express no opinion as to whether the laws of any particular jurisdiction are applicable to the subject matter hereof. We are not rendering any opinion as to compliance with any federal or state antifraud law, rule or regulation relating to securities, or to the sale or issuance thereof.

With regard to our opinion in clause (ii) below concerning the Agreement Shares, we have assumed that all Agreement Shares issuable pursuant to the Purchase Agreement are issued on the date hereof (notwithstanding any conditions or limitations restricting such exercise or issuance set forth in the Purchase Agreement).

COOLEY LLP 4401 EASTGATE MALL SAN DIEGO, CA 92121

T: (858) 550-6000 F: (858) 550-6420 COOLEY.COM

TRACON Pharmaceuticals, Inc.

March 27, 2017

Page Two

On the basis of the foregoing, and in reliance thereon, we are of the opinion that (i) the Shares are validly issued, fully paid and non-assessable and (ii) upon issuance and delivery of the Agreement Shares by the Company in accordance with the terms of the Purchase Agreement, including, without limitation, the payment in full of the applicable consideration therefor, the Agreement Shares will be validly issued, fully paid and non-assessable.

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

COOLEY LLP 4401 EASTGATE MALL SAN DIEGO, CA 92121

T: (858) 550-6000 F: (858) 550-6420 COOLEY.COM