This article proposes a dynamic model and a tracking control strategy for a dielectric elastomer (DE) actuator based on the model predictive controller (MPC). First, the dynamic model of the DE actuator is established, which can describe its asymmetric hysteresis, creep, and even rate-dependent hysteresis behaviors simultaneously. Then, on the basis of the established dynamic model, an inverse compensation controller (ICC) is designed to compensate the hysteresis and creep nonlinearities of the DE actuator on its tracking control. Moreover, the MPC is designed to cooperate with the ICC, which can overcome the influences of the modeling error and uncertainties on the control precision. Finally, several experiments demonstrate the effectiveness of the proposed dynamic model and control strategy.