An adaptive closed-loop control method for precision image stabilization based on active optical technology was proposed to compensate for low-frequency LOS disturbances in space astronomical telescopes. The fine guide sensor （FGS） was used as a high-precision LOS disturbance detector， and the four-point supporting large-aperture fast steering mirror （FSM） mechanism drove by piezoelectric actuators（PZT） was used as a LOS disturbance compensator in this method. First， a PID controller was connected in series with an integral link for precise image stabilization closed-loop control to obtain the two-dimensional swing angles of the FSM required to compensate for the two-dimensional LOS disturbance detected by FGS. Furthermore， the expansion amount of each PZT was calculated through driving structure. Then， the feedforward compensation method based on generalized Bouc-Wen inverse hysteresis model was used for high-precision positioning control of the piezoelectric ceramic actuator. Finally， according to supervised Hebb learning rules， the single neuron with self-learning and adaptive abilities was used to adjust the PID controller parameters， thereby obtaining the optimal controller parameters. The experimental results show that the proposed control method can effectively compensate the LOS disturbance of the space astronomical telescope， and the integral value of PSD of the position error of the star point centroid in the X direction and Y direction of the FGS can be suppressed by 98.54% and 98.62% respectively in the frequency band of 0~6 Hz.