Most previous works in the field of nonlinear memristive chaotic systems mainly focus on non‐material memristor while seldom on material memristor. In this letter, the model and the corresponding parameter identification of the Knowm memristor is presented. The chaotic circuit based on the Knowm memristor is designed. Equilibrium points and stability of this Knowm‐memristor‐based chaotic system is analyzed. Nonlinear dynamic behavior is presented by the bifurcation diagram and Lyapunov exponents. Finally, the hardware circuit of this Knowm‐memristor‐based chaotic system is designed and the experimental results are presented for confirmation.