In a precision pointing system for space laser communication, the hysteresis nonlinearity of the steering mirror driven by the piezoelectric actuator (PEA) can not only reduce its pointing accuracy greatly, but also affect the acquisition of beacon light and link stability. To address this issue, an improved Prandtl-Ishlinskii (P-I) model based on the PLAY hysteresis operator and a parameter identification method are presented, and on this basis, a feedforward linearized inverse compensation method for the steering mirror is proposed. In order to further improve the tracking accuracy of the system, on the basis of linearization, a static output feedback controller is designed to form a composite control method, and a laser communication terminal precision sighting system experiment is designed to verify the effectiveness of the composite method, in which sine signals with different frequencies and amplitudes are input. Experiment results show that the maximum fitting error of the improved P-I model is less than 1%. Inverse compensation of the feedforward model can reduce the linearity error of the PEA from 5% to less than 1%. Tracking errors of the system based on the compound method are reduced by 80%.