Giant magnetostrictive actuators show hysteresis and displacement nonlinear characteristics when they are used in the field of precision actuation control.To overcome the shortcomings,a kind of control strategy combined with the Cerebellar Model Articulation Controller(CMAC)feedforward inverse compensation and the fuzzy PID control was presented.A dynamic inverse model of the GMA was established with the CMAC on-line learning method to compensate the hysteresis nonlinearity of the GMA.A fuzzy PID controller was introduced in GMA to achieve the precision control of the GMA.Using this controller,the learning error of CMAC was decreased,the disturbance was eliminated and the tracking control performance of system was improved.The results came from simulation and experiments show that the control method can effectively reduce the hysteresis error and the tracking error of the system is less than 5% and the displacement tracking error is 0.58(mean square error).In addition,this strategy is characterized by learning and controling at the same time,so that the control system adapts to the changes in the dynamic characteristics of controlled object and has a stronger robustness.Meanwhile,it eliminates external interference effectively and improves its adaptive control performance.