Dielectric electro-active polymer (DEAP) actuator has been considered potentially in recent decades for many applications, especially in intelligent bio-inspired robotics. However, the viscoelastic properties including ratedependent and asymmetrical hysteresis, creep and the uncertainties under different operating conditions are still limiting its further development. In this paper, a feedforward-feedback tracking control approach is developed. Firstly, a long short term memory (LSTM) neural network combined with empirical mode decomposition (EMD), which has the information of reference as input and the control signal as output, is constructed using the data collected from the DEAP actuator. Thus, the well trained LSTM model can precisely capture the inverse hysteresis dynamics of the DEAP actuator, which can be used as a feedforward compensator to eliminate the hysteresis nonlinearities. Then, a conventional proportional-integral-derivative feedback controller is combined to compensate for the uncertainties and creep effect. To verify the effectiveness of the proposed feedforward compensator, comparative experiments on prediction of control signal and compensation of hysteresis among the traditional artificial back propagation neural network model, the inverse rate-dependent PrandtlIshlinskii model and the proposed LSTM-based compensator are conducted. The results validate that the LSTMbased compensator can precisely predict the control signal and eliminate the hysteresis with best performance indexes. Moreover, the tracking control experiments further validate the effectiveness of the proposed feedforward-feedback approach.