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Compared with PZT, the actuating circuit of giant magnetostrictive material (GMM) is easier to implement in engineering for its lower supply voltage. Though the strain of GMM is almost larger than PZT, it also needs to be amplified for practical applications. A press-bend amplification based giant magnetostrictive actuator (GMA) is designed for testing. The electromechanical system model for the GMA is presented, which consists of two subsystems, one is a rate-independent hysteretic model and the other is a linear transfer function with no hysteretic effect. The Prandtl-Ishlinskii (PI) model was employed for analyzing of the hysteresis in the GMA. Based on thoroughly discussion of the Prandtl-Ishlinskii model, an adaptive variable structure controller was designed, which ensured global stability of the control system and certain accuracy of tracking a desired trajectory. Both simulation and experiment results verified the correctness of the electromechanical model and the applicable of the proposed control method.