In this study, an integrative giant magnetostrictive material-based electro-hydrostatic actuator (GMEHA) was designed. Firstly, the uniform of magnetic field distribution on giant magnetostrictive material rod was obtained by using finite element method, i.e. the nonuniformity of the axis and radial direction magnetic field intensity were less than 3% and 0.05%, respectively. Secondly, the flow rate model through the reed valve model was established in COMSOL Multiphysics software, and the relevant properties of reed valves were studied. Thirdly, the dynamic mathematical model of GMEHA was systematically established based on the operational principles of the GMEHA, accordingly, and the simulation model of GMEHA was built in Matlab/Simulink. Finally, the model and simulation results were subsequently verified with the experimental data, which indicates the effective output stroke of the designed GMEHA reached 70 mm, and the maximum no-load output flow was 0.85 L/min at approximately 250 Hz with the best working frequency; the blocked force was nearly 120 N. These results demonstrated the accuracy of the theoretical model and provided a foundation for the design and optimization of the GMEHA.