Hysteresis and creep hinder the effective use of IPMC in sensors and actuators. In order to cope with these disadvantageous effects, a fundamental approach is inverse compensation. This paper presents a hybrid model of hysteresis and creep in piezoelectric actuator, which is constructed by Preisach operator and creep operator. Then, the corresponding inverse models for both hysteresis and creep are developed. Based on the obtained inverse model, a method for real-time compensation of the hysteresis and creep of piezoelectric actuator is applied to the control of system nonlinearities. The efficiency of this new model and the method of real-time inverse control are demonstrated by simulation and experiment based on an IPMC actuator. Using this control concept, the tracking errors caused by hysteretic and creep effects are reduced by approximately one order of magnitude, the result verified the validity of the model and effectiveness of the controller.