In order to compensate the inherent hysteresis nonlinearity and improve the precision of giant magnetostrictive actuator(GMA), a real-time hysteretic compensation control strategy was proposed, combining a cerebellar model articulation controller(CMAC) feedforward controller and a proportional integral derivative(PID) feedback controller,and the precision position tracking control of the GMA was realized. As CMAC neural network could not be used to approximate the multi-valued mapping of inverse hysteresis directly, an inverse hysteretic operator was proposed to transform the multi-valued mapping into a one-to-one mapping which enabled neural networks to approximate the behavior of inverse hysteresis. Simulation results showed that the proposed control strategy can adapt itself to the changes of the hysteretic characteristics of the GMA under different input reference signals,and that on-line inverse hysteresis model of the GMA can be obtained,and thus the hysteretic impact was eliminated and the high precision control of the GMA was achieved.