EX-5.1

Exhibit 5.1

650 Page Mill Road

Palo Alto, CA 94304-1050

PHONE 650.493.9300

FAX 650.493.6811

www.wsgr.com

September 24, 2018

Kodiak Sciences Inc.

2631 Hanover Street

Palo Alto, California 94304

Re:

Registration Statement on Form S-1

Ladies and Gentlemen:

This opinion is furnished to you in connection with the Registration Statement on Form S-1 (Registration No. 333-227237), as amended (the “Registration Statement”), filed by Kodiak Sciences Inc. (the “Company”) with the Securities and Exchange Commission in connection with the registration under the Securities Act of 1933, as amended, of 9,000,000 shares (including 1,350,000 shares issuable upon exercise of an option to purchase additional shares granted to the underwriters) of the Company’s common stock, par value $0.0001 per share (the “Shares”), to be issued and sold by the Company. We understand that the Shares are to be sold to the underwriters for resale to the public as described in the Registration Statement and pursuant to an underwriting agreement, substantially in the form filed as an exhibit to the Registration Statement, to be entered into by and among the Company and the underwriters (the “Underwriting Agreement”).

We are acting as counsel for the Company in connection with the sale of the Shares by the Company. In such capacity, we have examined originals or copies, certified or otherwise identified to our satisfaction, of such documents, corporate records, certificates of public officials and other instruments as we have deemed necessary for the purposes of rendering this opinion. In our examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity with the originals of all documents submitted to us as copies, the authenticity of the originals of such documents and the legal competence of all signatories to such documents.

We express no opinion herein as to the laws of any state or jurisdiction other than the General Corporation Law of the State of Delaware (including the statutory provisions and all applicable judicial decisions interpreting those laws) and the federal laws of the United States of America.

On the basis of the foregoing, we are of the opinion, that the Shares to be issued and sold by the Company have been duly authorized and, when such Shares are issued and paid for in accordance with the terms of the Underwriting Agreement, will be validly issued, fully paid and nonassessable.

AUSTIN BEIJING BOSTON BRUSSELS HONG KONG LONDON LOS ANGELES NEW YORK PALO ALTO

SAN DIEGO SAN FRANCISCO SEATTLE SHANGHAI WASHINGTON, DC WILMINGTON, DE