This paper aims to improve the control performance of the precision tracking system for laser communication by studying the control method of Fast Steering Mirrors (FSM) driven by a voice coil motor. FSM often face the problems of strong cross-coupling characteristics and external disturbances. To overcome these challenges, we propose a composite fast nonsingular terminal sliding mode control strategy integrating feedforward decoupling compensation and fixed-time extended state observer. First, the FSM’s coupling transfer function matrix model with double inputs and double outputs is established by using the system identification method, and the feedforward decoupling compensator is designed to compensate for the coupling components and achieve motion decoupling between the X-axis and Y-axis. Second, the fixed-time extended state observer is designed for each decoupled single-axis model to achieve a fixed-time estimation of angular velocity and external disturbances simultaneously. Then, the fast nonsingular terminal sliding mode surface is constructed, and the exponential power function is adopted to replace the sign function in control law design, so as to improve the system’s convergence speed and suppress the chattering of the sliding mode. The proposed control system’s stability and the tracking error finite-time convergence are proved based on the Lyapunov stability analysis method. Finally, the effectiveness of the proposed composite control strategy is verified by comparative experiments. The experimental results show that under the 100 Hz strong disturbances, for the FSM tracking 60 Hz and 120 Hz circular trajectories, the average absolute values of its trajectory tracking error are 0.0036° and 0.0131°, respectively, indicating that the system can maintain good tracking performance. The proposed composite control strategy is validated as effectively meeting the FSM’s high-precision and strong anti-disturbance requirements for laser communication.