In this paper, focusing on the application-oriented giant magnetostrictive material (GMM)-based electro-hydrostatic actuator, which features an applied magnetic field at high frequency and high amplitude, and concentrating on the static and dynamic characteristics of a giant magnetostrictive actuator (GMA) considering the prestress effect on the GMM rod and the electrical input dynamics involving the power amplifier and the inductive coil, a methodology for studying the static and dynamic characteristics of a GMA using the hysteresis loop as a tool is developed. A GMA that can display the preforce on the GMM rod in real-time is designed, and a magnetostrictive model dependent on the prestress on a GMM rod instead of the existing quadratic domain rotation model is proposed. Additionally, an electrical input dynamics model to excite GMA is developed according to the simplified circuit diagram, and the corresponding parameters are identified by the experimental data. A dynamic magnetization model with the eddy current effect is deduced according to the Jiles-Atherton model and the Maxwell equations. Next, all of the parameters, including the electrical input characteristics, the dynamic magnetization and the mechanical structure of GMA, are identified by the experimental data from the current response, magnetization response and displacement response, respectively. Finally, a comprehensive comparison between the model results and experimental data is performed, and the results show that the test data agree well with the presented model results. An analysis on the relation between the GMA displacement response and the parameters from the electrical input dynamics, magnetization dynamics and mechanical structural dynamics is performed.