Smart material electrohydrostatic actuator based on giant magnetostrictive transducer can meet the requirements of smaller vehicles like the unmanned combat air vehicle as well as in rotating environments like helicopter rotors. In order to analyze and improve the performance of smart material electrohydrostatic actuator, the dynamic hysteresis nonlinear model of giant magnetostrictive transducer is developed based on the relationship between complex permeability and magnetic energy power loss in giant magnetostrictive material, and the inverse model is also derived to design the inverse compensator for improving the linearity of giant magnetostrictive transducer. The experiments show that with the help of inverse compensator, phase lag between the input control signal and the output displacement of giant magnetostrictive transducer is decreased. In addition, the simulation results show that because of the effect of inverse compensator, the flow rate is increased and the growth rate increases with the increase of excitation frequency.