The influence of unmeasurable disturbances in a fast-steering mirror system must be considered to improve the beam-tracking performance of a compound-axis system. For measurable disturbances, an adaptive feedforward control algorithm is designed. Inspired by this, an adaptive inversion proportional-integral-derivative(PID) control system for suppressing unmeasurable disturbances was designed. An adaptive algorithm was used to improve the steady-state accuracy of the system and the adaptability to different disturbances. In addition, a PID controller was used to further correct the error signals and improve the dynamic performance of the system. The simulation results show that compared with that of the PID control algorithm, the mean square difference of the error of the adaptive inversion PID control system decreases by 34.76%. Compared with that of the adaptive control algorithm, the mean square difference of the error of the adaptive inversion PID control system decreases by 13.3%. The accuracy of the compound control system significantly improved compared with that of the classical PID and adaptive control systems. When using the compound algorithm, the rise time decreases by 48.9% compared with the adaptive algorithm, and the overshoot decreases by 80.5% compared with the classical PID algorithm. Overall, the dynamic performance of the system improved significantly.