Aiming at the dynamic hysteresis of piezoelectric stack actuator (PA) between input voltage and output displacement, the dynamic hysteresis model which based on the asymmetric BoucWen hysteresis model was established;the six parameters of hysteresis model was recognized by the particle swarm algorithm. To improve dynamic output displacement of PA,the hysteresis inverse model was derived;the feedforward control was used to compensate the hysteresis. The results of simulation and experiment showed that when PA was driven by 0~120 V input peak voltage or 0~500 Hz driven frequency, the dynamic hysteresis model can well reflect and forecast the output dynamic displacement. The feedforward compensation experiment result shows that the feedforward compensation based on the inverse model can decreased the area of hysteresis loop and the nonlinearity of output displacement is decreased about 3%.