Giant Magnetostrictive Actuator(GMA) has complex hysteretic nonlinearities, which can degrade system performance and cause system instability. To solve the problem, this paper establishes a model to accurately describe hysteretic phenomenon and propose a proper method to improve real-time control accuracy. Firstly, Prandtl-Ishlinskii(PI) operator is proposed in this paper to model the hysteresis of GMA and Least Mean Square(LMS) algorithm is used identify the parameter of this model, by which the prediction error reaches up to 0.037 9 μm. Then, an inverse model is established based on the PI model for real-time compensation control of the hysteresis, and the inverse control error reaches up to 0.309 μm. The experimental results demonstrate that PI operator can accurately characterize the GMA hysteresis, and the model has advantages of simple calculation and strong hysteretic tracking ability. The real-time compensation control of hysteresis can effectively reduce hysteretic errors and improve real-time control accuracy. It is a effective way to achieve precision driving control of GMAs.