Human trajectory prediction is challenging and critical in various applications (e.g., autonomous vehicles and social robots). Because of the continuity and foresight of the pedestrian movements, the moving pedestrians in crowded spaces will consider both spatial and temporal interactions to avoid future collisions. However, most of the existing methods ignore the temporal correlations of interactions with other pedestrians involved in a scene. In this work, we propose a Spatial-Temporal Graph Attention network (STGAT), based on a sequence-to-sequence architecture to predict future trajectories of pedestrians. Besides the spatial interactions captured by the graph attention mechanism at each time-step, we adopt an extra LSTM to encode the temporal correlations of interactions. Through comparisons with state-of-the-art methods, our model achieves superior performance on two publicly available crowd datasets (ETH and UCY) and produces more "socially" plausible trajectories for pedestrians.