This paper proposes a dynamic model for dielectric elastomer actuators (DEAs) based on the long-short term memory (LSTM) deep neural network. The fabrication of the DEA and the framework of the experimental platform are introduced firstly. The behaviors of the DEA are analyzed through several sets of experiments, which shows the DEA has obvious memory behavior (i.e., the hysteresis behavior and creep behavior), where the hysteresis behavior is a symmetry and rate-dependence. Considering that the traditional neural network is difficult to describe the memory property, the LSTM deep neural network is constructed as the dynamic model of the DEA. Then, such neural network is trained according to the experimental data. Finally, the comparation results of the experimental data and the model output verify the effectiveness as well as the generalization ability of the dynamic model.