Vehicle trajectory prediction technology is of great significance in autonomous driving and intelligent transportation systems. Ego-vehicles can judge the future motion state considering nearby vehicles by predicting their trajectories, which facilitates safe and effective decisions to avoid collisions. It is a challenging task to accurately predict the future trajectories of surrounding vehicles. To solve this problem, we propose a Self-Attention Social Generative Adversarial Networks (SA-SGAN) model to predict trajectories of surrounding vehicles. We use the Self-Attention mechanism to capture the correlation between the features in the vehicle trajectory sequence to effectively solve the problem of missing important information due to a long input sequence, and use training characteristic of Generative Adversarial Networks (GAN) to effectively learn the distribution of real trajectory data and improve prediction accuracy. We evaluate the proposed model through NGSIM dataset, use the trained model to investigate the vehicle trajectory in the next 5s in a three-segment scenario of the US-101 highway, and use the Average Displacement Error (ADE) and Final Displacement Error (FDE) as the evaluation indicators. Compared with baseline methods, the proposed model reduces the evaluation indicators to 4.97 and 8.92 respectively.