Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statement (No. 333-213926) on Form S-3 and Registration Statement (No. 333-203703, No. 333-210369, No. 333-216858 and No. 333-224062) on Form S-8 of KemPharm, Inc. of our report dated March 1, 2019, 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, 2018.

/s/ RSM US LLP

Orlando, Florida

March 1, 2019