The invention provides a bidirectional multistable dielectric elastomer driver. The bidirectional multistable dielectric elastomer driver includes a housing, a dielectric elastomer driving band, an execution shaft and an execution block, wherein the dielectric elastomer driving band, the execution shaft and the execution block are arranged in the housing; the execution block is connected with the inner wall of the housing through the dielectric elastomer driving band; a dielectric elastomer driving band is arranged in an X-shape to fix the execution block at the central position of the housing; the upper side, the lower side, the left side and the right side of the housing are each provided with a fixed magnet unit; the execution shaft penetrates through the execution block in the forward and backward direction of the housing; and the front side and the back side of the housing are provided with circular through holes. The bidirectional multistable dielectric elastomer driver has the advantages of being compact in structure, realizing execution and switching of five stable states in two directions in the plane, being light in weight, being quiet in operation, being quick in response, being convenient to control and being high in accuracy of control, reducing energy consumption, reducing the possibility of losing stable state and being broken for the dielectric elastomer film, and increasing the driving range in the plane of the driver.