To achieve the tracking control objective of the dielectric elastomer actuator (DEA), this paper proposes the fractional order modeling method and the fractional order internal model control method. Firstly, a fractional order transfer function (FOTF) model of the DEA is built to depict its complex "memory" property. Then, to achieve the computer control, an integer order approximation model (IOAM) of the FOTF model is built by using the Oustaloup filter. Considering that the order of the IOAM is too high, a reduced integer order approximation model is established by using the Ramer-Douglas-Peucker line simplification algorithm to facilitate the system controller design. Next, a fractional order internal model controller (FOIMC) is designed, and a reduced integer order approximation controller of the FOIMC is developed. Finally, some experiments are exerted to demonstrate the effectiveness of the proposed control method.