Predicting traffic agent trajectories plays an important role in autonomous driving, traffic operations, transportation safety analysis, etc. Although many deep learning algorithms are devised to predict future agent trajectories, the trajectory prediction problem is still challenging due to the complexity of decision-making process, interactions with surrounding vehicles, and the existence of multiple possible intentions for the traveling agents even under similar scenarios. Most existing methods are limited by the requirement of graph structures (e.g., Graph Neural Network) or the requirement of manually labeled intentions. In this study, we propose a pure Transformer-based deep learning model for multi-modal trajectory prediction considering temporal dependencies and agent-agent spatial interactions. After encoding the historical trajectories, two parallel decoders are employed to generate trajectories and probabilities on separate decoder tracks. The model is evaluated on two real-world datasets, one highway dataset and the other pedestrian dataset with solid performance. One important insight is that following a ``propose-then-select'' strategy, the agent-agent spatial interactions are only considered for probability estimation instead of trajectory generation. In summary, the proposed model provides a potential direction to design more robust and effective multi-modal trajectory prediction models.

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