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Trajectory prediction has been a long-standing problem in intelligent systems like autonomous driving and robot navigation. Models trained on large-scale benchmarks have made significant progress in improving prediction accuracy. However, the importance on efficiency for real-time applications has been less emphasized. This paper proposes an attention-based graph model, named GATraj, which achieves a good balance of prediction accuracy and inference speed. We use attention mechanisms to model the spatial-temporal dynamics of agents, such as pedestrians or vehicles, and a graph convolutional network to model their interactions. Additionally, a Laplacian mixture decoder is implemented to mitigate mode collapse and generate diverse multimodal predictions for each agent. GATraj achieves state-of-the-art prediction performance at a much higher speed when tested on the ETH/UCY datasets for pedestrian trajectories, and good performance at about 100 Hz inference speed when tested on the nuScenes dataset for autonomous driving. We conduct extensive experiments to analyze the probability estimation of the Laplacian mixture decoder and compare it with a Gaussian mixture decoder for predicting different multimodalities. Furthermore, comprehensive ablation studies demonstrate the effectiveness of each proposed module in GATraj. The code is released at https://github.com/mengmengliu1998/GATraj.