In order to improve the tracking accuracy of ATP （acquisition，tracking，pointing） control system for space optical communication，the ATP servo control system is analyzed at first. Considering the transmission characteristic and motor time-delay，the SISO compensator is used to make the system response more quickly. A new Smith predictive control is presented considering the transmission characteristic of fine tracking system and the fast steering mirror time-delay. It is simulated with MATLAB，and the obtained results are compared with that of the conventional PID controllers. The simulation results show that the new control method has obvious advantages for time delay control，and has good match feature with PID，PI and PD control. The system is a good solution to the instability caused by the pure time delay. It has better robustness and anti-interference features.