Exhibit 5.1

May 16, 2017

G1 Therapeutics, Inc.

79 T.W. Alexander Drive

4501 Research Commons, Suite 100

Research Triangle Park, NC 27709

Ladies and Gentlemen:

We have acted as legal counsel to G1 Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) of (i) a Registration Statement (No. 333-217285) on Form S-1 (the “Initial Registration Statement”), and (ii) a second Registration Statement on Form S-1 filed pursuant to Rule 462(b) under the Securities Act of 1933, as amended (the “Securities Act”) (the “462(b) Registration Statement”), pursuant to which the Company is registering the offering for sale under the Securities Act of up to an aggregate of 862,500 additional shares (the “Shares”) of the Company’s common stock, par value $0.0001 per share (the “Common Stock”).

The Shares are to be sold by the Company pursuant to an underwriting agreement (the “Underwriting Agreement”) to be entered into by and among the Company and J.P. Morgan Securities LLC and Cowen and Company, LLC, as representatives of the several underwriters to be named therein. The form of the Underwriting Agreement has been filed as Exhibit 1.1 to the Initial Registration Statement. This opinion is being rendered in connection with the filing of the 462(b) Registration Statement with the Commission. All capitalized terms used herein and not otherwise defined shall have the respective meanings given to them in the 462(b) Registration Statement.

In connection with this opinion, we have examined the Company’s Fifth Amended and Restated Certificate of Incorporation, as amended, and Bylaws, each as currently in effect, and the form of the Underwriting Agreement; such other records of the corporate proceedings of the Company and certificates of the Company’s officers as we have deemed relevant; the Initial Registration Statement and the exhibits thereto; and the 462(b) Registration Statement and the exhibits thereto.

In our examination, we have assumed the genuineness of all signatures, the legal capacity of natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified or photostatic copies and the authenticity of the originals of such copies.

Our opinion is limited to the General Corporation Law of the State of Delaware and we express no opinion with respect to the laws of any other jurisdiction. No opinion is expressed

MINTZ, LEVIN, COHN, FERRIS, GLOVSKY AND POPEO, P.C.

G1 Therapeutics, Inc.

May 16, 2017

Page 2

herein with respect to the qualification of the Shares under the securities or blue sky laws of any state or any foreign jurisdiction.

Please note that we are opining only as to the matters expressly set forth herein, and no opinion should be inferred as to any other matters. This opinion is based upon currently existing statutes, rules, regulations and judicial decisions, and we disclaim any obligation to advise you of any change in any of these sources of law or subsequent legal or factual developments which might affect any matters or opinions set forth herein.

Based upon the foregoing, we are of the opinion that the Shares, when issued and sold in accordance with the form of the Underwriting Agreement most recently filed as an exhibit to the Initial Registration Statement and the prospectus that forms a part of the Initial Registration Statement, will be validly issued, fully paid and non-assessable.

We understand that you wish to file this opinion with the Commission as an exhibit to the 462(b) Registration Statement in accordance with the requirements of Item 601(b)(5) of Regulation S-K promulgated under the Securities Act and to reference the firm’s name under the caption “Legal Matters” in the prospectus which is incorporated by reference in the 462(b) Registration Statement, and we hereby consent thereto. In giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Mintz, Levin, Cohn, Ferris,

Glovsky and Popeo, P.C.

Mintz, Levin, Cohn, Ferris,

Glovsky and Popeo, P.C.