Exhibit 5.1

Sean M. Clayton

T: +1 858 550 6034

sclayton@cooley.com

September 6, 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 offering by the Company of $11,550,332 of shares of the Company’s common stock, par value $0.001 (the “Shares”), pursuant to a Registration Statement on Form S-3 (No. 333-209313) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), the prospectus included within the Registration Statement (the “Base Prospectus”), and the prospectus supplement to be filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations of the Act (the “Prospectus Supplement” and together with the Base Prospectus, the “Prospectus”).  The Shares are to be sold by the Company in accordance with a Capital on Demand^TM Sales Agreement, dated September 6, 2018, between the Company and JonesTrading Institutional Services LLC (the “Agreement”), as described in the Prospectus.

In connection with this opinion, we have examined and relied upon the Registration Statement and the Prospectus, the Agreement, the Company’s Amended and Restated Certificate of Incorporation, as amended, its Amended and Restated 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.  In rendering this opinion, we have assumed the genuineness and authenticity of all signatures on original documents; the genuineness and authenticity of all documents submitted to us as originals; the conformity to originals of all documents submitted to us as copies; and the accuracy, completeness and authenticity of certificates of public officials.

We have assumed (i) that each sale of Shares will be duly authorized by the Board of Directors of the Company, a duly authorized committee thereof or a person or body pursuant to an authorization granted in accordance with Section 152 of the General Corporation Law of the State of Delaware (the DGCL”), (ii) that no more than 11,000,316 Shares will be sold under the Agreement and (iii) that the price at which the Shares are sold will equal or exceed the par value of the Shares.  We express no opinion to the extent that future issuances of securities of the Company and/or anti-dilution adjustments to outstanding securities of the Company cause the number of shares of the Company’s common stock outstanding or issuable upon conversion or exercise of outstanding securities of the Company to exceed the number of Shares then issuable under the Agreement.

Cooley llp   4401 Eastgate Mall   San Diego, CA   92121
t: (858) 550-6000  f: (858) 550-6420  cooley.com

Our opinion herein is expressed solely with respect to the General Corporation Law of the State of Delaware.  Our opinion is based on these laws as in effect on the date hereof.  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 against payment therefor in accordance with the Agreement, 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 and to the filing of this opinion as an exhibit to the Company’s Annual Report on Form 10-K to be filed with the Commission for incorporation by reference into the Registration Statement.

Very truly yours,

Cooley llp

By: /s/ Sean M. Clayton

Sean M. Clayton

Cooley llp   4401 Eastgate Mall   San Diego, CA   92121
t: (858) 550-6000  f: (858) 550-6420  cooley.com