To improve the output performance of embedded giant magnetostrictive actuators (GMAs) for non-circular hole precision machining and to describe the transient nonlinear hysteresis behavior of giant magnetostrictive material (GMM), the magnetostrictive process of GMM is analyzed in detail in this paper. Based on the J–A model and the Gibbs free energy model, a transient multi-field coupling model of GMM is developed by considering the eddy current effect, compression stress variation, and ΔE effect. The simulation results show that the hysteresis loop area increases with increasing driving frequency. The strain of GMM increases first and then decreases with increasing preloading stress. If the stiffness of the deformable bar is too large, the stress of GMM will increase rapidly, thus hindering the elongation of GMM. The simulation process combines the magneto-mechanical coupling model and the dynamic model of embedded GMAs. The simulation results at different excitation frequencies are basically consistent with the experimental data, indicating that the proposed model can predict the output displacement well and provide a theoretical basis for the optimized design of magneto-mechanical coupling for high-performance embedded GMAs.