Piezoelectric fast steering mirror (PZT FSM) is the core component of the fine tracking system for space laser communication, and its actuator is a piezoelectric ceramic. Consequently, there is a hysteretic nonlinear disturbance throughout the entire range of the FSM’s steering. To enhance the fine tracking system’s performance, this paper innovatively analyzes and verifies the effect of the PZT FSM hysteresis characteristics on the error suppression bandwidth of the fine tracking system. Firstly, the rate-dependent hysteresis model is established by serially connecting the Prandtl–Ishlinskii (P-I) model with the dynamic linear mode. The inverse model is designed as a feedforward controller, followed by the conduction of open-loop feedforward compensation experiments. Subsequently, we propose a compound control method based on the rate-dependent hysteresis mode and conduct a simulation analysis. Finally, the experimental platform for the fine tracking system is set up, and the optimization effect of compensating for hysteresis nonlinearity on the fine tracking system is verified. The experimental results show that the nonlinearity of the PZT FSM is improved by 30% in the middle- and high-frequency ranges, and the error suppression bandwidth of the fine tracking system is improved by 41.7%. This effectively enhances the fine tracking system’s error suppression capability.