Hysteresis of a piezoelectric actuator is rate-dependent, but most hysteresis models are based on elementary rate-independent models, which are not suitable for modeling actuator behavior across a wide range of frequencies. This paper presents a novel modified inverse Preisach model to compensate the hysteresis of a piezoelectric actuator at varying frequency ranges. The classical Preisach model for hysteresis is introduced first, the identification of \mu-function through least square method is conducted afterwards. The linearity property of the Preisach model is analyzed and verified by experiment. A novel modified inverse Preisach model featured with weighed sum of μ -density functions is proposed, which is based on the linearity property. The fast Fourier transform method is adopted to select the proper μ-density functions and weights to form a real-time online rate-dependent compensator for piezoceramic (PZTs) hysteresis. During experiments with tracking multifrequency composed signals, we have observed that the hysteresis features of the PZT can be consistently compensated. The experimental results show that the proposed open-loop hysteresis adjust method greatly improves the tracking control accuracy of the PZT.