On the basis of analyzing Moving Average(MA) correction mechanism, random deviations of laser beams are adjusted with the compensation and the moving average of compensation in this paper. Take the progress of adjusting random deviations of pulse laser beams with fast steering mirrors in the beam delivery system as an example. Closed-loop control algorithms for beams stabilization based on MA are introduced. The simulation results are presented, and the correction effects with the ground vibrations or not are illustrated. The outcomes indicate that algorithms based on MA will control the random drifts effectively, which prove that the optimal MA can be reduced to 1/15 times. Meanwhile, these methods which can achieve real-time control are practical. The key of applications lies in construction of the appropriate correction formula.