Abstract: In order to analyze the non-linear dynamic characteristic in electromagnetic (EM) field and mechanical field exactly, it is key to establish a proper multi-physics coupling model for giant magnetostrictive actuator (GMA). Considering the eddy current effect, this paper presents a dynamic EM-mechanical strongly coupled model for GMA based on the energy variational principle. A prototype is built so that the axial displacements under different frequencies are measured. The results show that there is only a 5% relative error between the calculated results and the experimental ones, which indicates that the proposed EM-mechanical strongly coupling numerical model is valid.