Soft robots have recently received much attention with their infinite degrees of freedoms and continuously deformable structures, which allow them to adapt well to the unstructured environment. A new type of soft actuator, namely, dielectric elastomer actuator (DEA) which has several excellent properties such as large deformation and high energy density is investigated in this study. Furthermore, a DEA-based soft robot is designed and developed. Due to the difficulty of accurate modeling caused by nonlinear electromechanical coupling and viscoelasticity, the iterative learning control (ILC) method is employed for the motion trajectory tracking with an uncertain model of the DEA. A D2 type ILC algorithm is proposed for the task. Furthermore, a knowledge-based model framework with kinematic analysis is explored to prove the convergence of the proposed ILC. Finally, both simulations and experiments are conducted to demonstrate the effectiveness of the ILC, which results show that excellent tracking performance can be achieved by the soft crawling robot.