Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statements (No. 333-234235 and No. 333-213926) on Form S-3 and Registration Statements (No. 333-203703, No. 333-210369, No. 333-216858, No. 333-224062 and No. 333-230041) on Form S-8 of KemPharm, Inc. of our report dated February 28, 2020 relating to the financial statements of KemPharm, Inc., appearing in this Annual Report on Form 10-K of KemPharm, Inc. for the year ended December 31, 2019.

/s/ RSM US LLP

Orlando, Florida

February 28, 2020