We propose a novel approach for recapturing targets as quickly as possible after the space-borne ATP (Acquisition, Tracking, and Pointing) system target loss in free-space laser communication. The approach uses past angular information to predict the target trajectory. An optimized finite memory filter is designed as the prediction algorithm. To obtain optimal prediction performance, the designed filter determines the filter parameters of different curve parts during offline training, and the parameters are adjusted according to the curve characteristics during predictive filtering. Simulation results indicate prediction accuracy above 0.1 degrees within 5 seconds. An experimental system was constructed in the lab to simulate the reacquisition process using a dynamic target and a real ATP system. Experimental results show that, compared with the classical orbit prediction method, this approach can effectively yield shorter acquisition times.