Abstract: A Preisach model is constructed for the hysteresis and nonlinearity of the giant magnetostrictive actuator, and the numerical format is given in F function method. With hysteresis and nonlinear being system disturbances, a novel nonlinear adaptive compensation algorithm is presented to accelerate the convergence speed which is the weakness in conventional comensation control of the giant magnetostrictive actuator. Steady-state error is taken as one reference input when solving the inverse of Preisach model and the sigmoid function is introduced into the variable step algorithm. Simulation and experiment research reveal that the new iterative algorithm presented has high precision of position control as well as faster convergence speed compared with the conventional feedforward compensation control.