The present paper considers a design of fish fin actuators based on shape memory alloy composites composed of a couple of plates with the opposite functions. Both SMA plates, whose microstructure is either martensite or austenite, are individually arranged in parallel and operated as a bias to each other. The actuation mechanism is based on change in elastic constant, from stiff to soft during austenite to martensite transformation. First, a preliminary model of the elastic and superelastic deformation is proposed for prediction of the optimum curvature of SMA plates, which enable us to control the steering of an underwater object. The analytical model provides the relationship between the bending moment and the curvature for the composite plates in each deformation range. For a given velocity of a moving fish robot, the underwater curvature and bending moment of its plates is successfully obtained. We design such a fish fin actuator made of a set of different types of SMA composite plates which are embedded in an elastometer matrix to form a fish tail fin.