Abstract: Fast steering mirror (FSM) driven by piezoelectric actuator has been widely used in multifarious precision instruments for stabilization and tracking systems, whose tracking accuracy is decided by the control accuracy of FSM. However, there is a seriously nonlinear interference of hysteresis in the driving of piezoelectric actuator. In response to this defect, an adaptive radial bass function (RBF) neural network was used to approximate the nonlinear interference of hysteresis, and based on which, the sliding mode control and backstepping algorithm were combined to design adaptive backstepping sliding mode (ABSM) controller. The simulation results show that, compared with the control accuracy of the sliding mode controller, the maximum tracking error and mean-root-square error of ABSM controller declines by 57.26% and 52.53% respectively, which improves the control accuracy of FSM evidently.