Dielectric elastomer actuators (DEAs) have been widely employed to drive various soft robots, due to their quiet fast muscle-like behavior. It is significant but challenging to model and control these soft actuators, due to their viscoelastic property, irregular geometry, complex structure, etc. In this paper, we propose a data-driven sparse identification method to discover the hidden governing equations of DEAs. These equations can help us interpret the nonlinear properties of DEAs. Due to their low computational cost, we can further use these equations to explore classic model-based control methods for real-time accurate control of viscoelastic DEAs. The experiments show that the proposed method can model the viscoelastic behavior of the DEAs with reasonable accuracy. A feedforward controller is finally developed to validate the effectiveness of the proposed method. It is expected that this modeling method can pave the way for accurate control of soft actuators/robots with structural and material nonlinearities.