Due to the influence of magnetic hysteresis and energy loss inherent in giant magnetostrictive materials(GMM), output displacement accuracy of giant magnetostrictive actuator(GMA) can not meet the precision and ultra precision machining. Using a GMM rod as the core driving element, a GMA which may be used in the field of precision and ultra precision drive engineering is designed through modular design method. Based on the Armstrong theory and elastic Gibbs free energy theory, a nonlinear magnetostriction model which considers magnetic hysteresis and energy loss characteristics is established.Moreover, the mechanical system differential equation model for GMA is established by utilizing D’Alembert’s principle. Experimental results show that the model can preferably predict magnetization property, magnetic potential orientation, energy loss for GMM. It is also able to describe magnetostrictive elongation and output displacement of GMA. Research results will provide a theoretical basis for solving the dynamic magnetic hysteresis,energy loss and working precision for GMA fundamentally. Due to the influence of magnetic hysteresis and energy loss inherent in giant magnetostrictive materials (GMM), output displacement accuracy of giant magnetostrictive actuator (GMA) can not meet the precision and ultra precision machining. Using a GMM rod as the core driving element, a Based on the Armstrong theory and elastic Gibbs free energy theory, a nonlinear magnetostriction model which conceives magnetic hysteresis and energy loss characteristics is established. Moreover , the mechanical system differential equation model for GMA is established by utilizing D’Alembert’s principle. Experimental results show that the model can preferably predict magnetization property, magnetic potential orientation, energy loss for GMM. It is also able to describe magnetostrictive elongation and output displacement of GMA. Research results will provide a theoretical basis f or solving the dynamic magnetic hysteresis, energy loss and working precision for GMA fundamentally.