Due to the presence of air turbulence in free-space optical (FSO) links, random fluctuations in wavefront phase and amplitude of the optical signal are reduced after it propagates through the air channel, which degrades the performance of free-space optical communication (FSOC) systems. Phase screen reflects the phase distortions resulting from air turbulence. Accordingly, accurate prediction with respect to phase screen is of significance for the FSOC. In this paper, we propose a phase screen prediction method based on the deep phase network (DPN). The advantages of the proposed method include strong robustness against air turbulence, low model depth, and fewer parameters as well as low complexity. The results reveal that our DPN enables desired inference accuracy and faster inference speed compared with the existing models, by combining the mean square deviation loss function with the pixel penalty terms. More concretely, the accuracy of phase screen prediction can reach up to 95%; further, the average time consumed to predict the phase screen is in the order of milliseconds only under various turbulence conditions. Also, our DPN outperforms the traditional Gerchberg-Saxton algorithm in convergence speed.