Point ahead angle (PAA) prediction is important in space laser communication, but the existing methods have low accuracy and complicated calculation processes. In this paper, a new PAA prediction method is proposed based on Kalman filtering of the optical axis pointing trajectory. The proposed method uses the high precision of fine tracking to improve the accuracy of predictive filtering. Taking ground-satellite laser communication as the research background, the beam transmission process in a typical acquisition, pointing, and tracking (APT) system is derived, then the Kalman filter model is established, and a simulation of the model is performed. The results show that the PAA can be predicted accurately and the error of the PAA can be reduced effectively the maximum prediction error is 3.8 mu rad only, and the method does not need to take the complex satellite perturbations into consideration. The proposed approach improves the accuracy of PAA prediction and contributes to the design of space laser communication systems.