Soft actuators have played an indispensable role in generating compliant motions of soft robots. Among the various soft actuators explored for soft robotic applications, dielectric elastomer actuators (DEAs) have caught the eye with their intriguing attributes similar to biological muscles. However, the control challenge of DEAs due to their strong nonlinear behaviors has hindered the development of DEA-based soft robots. To overcome the control challenge, this paper proposes a bioinspired control approach of DEAs. A three-dimensional muscle-like DEA, capable of large forces and giant deformation, is fabricated and adopted as the control platform. To facilitate the controller design, the dynamic model of the DEA is developed through experimental analysis, which takes electromechanical coupling, viscoelastic effects and dynamics uncertainties into consideration. Motivated by the proprioception of the biological muscles, the self-sensing capability of the actuator is explored and exhibits good accuracy. Thus the self-sensing of the actuator is utilized to provide the sensory feedback in the control loop without the need of additional external sensors. Inspired from the role of the cerebellum in motor learning, a cerebellum model articulation nonlinear controller is proposed to compensate the dynamics uncertainties and to provide motion correction. Finally, the effectiveness of the proposed control approach is verified by both the simulation and the experiments.