Abstract: This paper proposes a new adaptive control method with viscoelastic hysteresis compensation for high-precision tracking control of dielectric elastomer actuators (DEAs). A direct inverse feedforward compensator is constructed by using a modified Prandtl-Ishlinskii model for compensating hysteresis nonlinearities. The dynamics effects of DEAs and disturbances are coped with the adaptive inverse controller using filtered-x normalized least mean square algorithm. A series of real-time tracking experiments are carried out on a DEA made of commercial acrylic elastomers. The proposed control method achieves accurate tracking of various trajectories with the relative root-mean-square tracking error ranging from 1.37% to a maximum of 4.37% over the whole operating frequency range, and outperforms previously proposed methods in terms of accuracy. The excellent tracking results demonstrate the effectiveness of the developed control method for dielectric elastomer artificial muscles based soft actuators.