Self-driving or autonomous vehicles need to efficiently and continuously navigate in complex traffic environments by analyzing the surrounding scene, understanding the behavior of other traffic-agents, and predicting their future trajectories. The main goal is to plan a safe motion and reduce the reaction time for possibly imminent hazards. A critical and challenging problem considered in this paper is to explore the movement patterns of surrounding traffic-agents and accurately predict their future trajectories for helping the vehicle make reasonable decision. To solve the problem, a deep learning-based framework is proposed in this paper for predicting trajectories of autonomous vehicles. The key is to train a social GAN (generative adversarial network) deep model for prediction of vehicle trajectory. The presented experimental results have verified that the proposed social GAN-based approach outperforms the traditional Social LSTM (long short-term memory)-based method.