The giant magnetostrictive actuator (GMA) has some advantages, such as fast response, high output force and high magnetic coupling coefficient, and so on. However, the magnetostrictive model of the GMA exists of characterisitic of hysteresis nonlinearity. The magnetostrictive mathematic model building is main task in the GMA design process, which can accurately describe its hysteresis nonlinearity. In order to effectivly improve the design efficiency of the GMA, the nonlinear constitutive model of GMA was established and governing equation of mechanical stress field in weak solutions is deduced, based on the magnetostrictive mechanism of the GMA and combined with JilesAtherton hysteresis model with piezomagnetic equation. Finally, based on the finite element method (FEM), the simulation process of the GMA model was realized in the COMSOL Multiphysics with a multiphysical field coupling software platform. A high efficient design method of GMA is obtained.