This paper proposes a dielectric elastomer (DE) soft actuator with sensing function, which can achieve synchronous measurement and control of membrane structures surfaces. Firstly, the dynamic model of electric driven process of the DE actuator is established, which can describe its electro-mechanical coupling behavior. Then, the parameters of the dynamic model are identified by a series of experiments. Moreover, the influence of some model parameters on dynamic responses of the DE actuator are analyzed to understand its basic dynamic characteristics. Next, the simplified circuit model for self-sensing process of the DE actuator is established, and the relationship between the electrical parameters and displacement of the DE actuator was calibrated experimentally. Finally, experiments of adaptive control of membrane surface are carried out, and the corresponding control strategy is designed. Experimental results indicate that the DE actuator has high precision in both actuation and sensing. Therefore, the DE soft actuator is highly promising in construction of high-precision space membrane antennas.