The dielectric elastomer actuator (DEA) is an intelligent device with an actuation-sensing integration capacity, which exhibits prospective applications in the field of soft robotics. Previous studies mainly focus on the actuation capacity of the DEA, while the studies on its sensing capacity and the practical realization of its actuation-sensing integration still confront great challenges. This article presents a self-sensing motion control scheme to realize the tracking control objective of the DEA, thus leaving out the use of the external displacement sensor. First, a self-sensing model of the DEA is established based on the nonlinear autoregressive with exogenous inputs (NARX) neural network to predict its own displacement. Then, by adopting the dynamic model of the DEA as the control object, a simulation environment based on the iterative learning control architecture is built to obtain the feedforward control sequence for tracking a target trajectory. Next, to enhance the control quality, the proportional–integral feedback controller is designed to combine with the feedforward control sequence to handle the uncertainties in practical experiments, in which the feedback signal is the output of the self-sensing model. Finally, several trajectory tracking control experiments are performed. The maximum value of the relative root-mean-square errors for all experimental results is less than 3.60%, which illustrates the effectiveness of the presented self-sensing motion control scheme.