Exhibit 5.1

Goodwin Procter LLP 100 Northern Avenue Boston, MA 02210   goodwinlaw.com +1 617 570 1000

September 18, 2020

Compass Therapeutics, Inc.

245 First Street

3^rd Floor

Cambridge, Massachusetts 02142

Re:    Securities Registered under Registration Statement on Form S-1

We have acted as counsel to you in connection with your filing of a Registration Statement on Form S-1 (as amended or supplemented, the “Registration Statement”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration by Compass Therapeutics, Inc., a Delaware corporation (the “Company”) of up to 52,127,041 shares (the “Shares”) of the Company’s Common Stock, $0.0001 par value per share, to be sold by the selling stockholders listed in the Registration Statement under “Selling Stockholders”.

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinions set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinions set forth below, on certificates of officers of the Company.

The opinion set forth below is limited to the Delaware General Corporation Law.

Based on the foregoing, we are of the opinion that the Shares have been duly authorized and validly issued and are fully paid and non-assessable.

We hereby consent to the inclusion of this opinion as Exhibit 5.1 to the Registration Statement and to the references to our firm under the caption “Legal Matters” in the Registration Statement. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

Very truly yours,

/s/ Goodwin Procter LLP

GOODWIN PROCTER LLP