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Accurate travel time prediction between two locations is one of the most substantial services in transport. In travel time prediction, origin–destination (OD) method is more challenging since it has no intermediate trajectory points. This paper puts forward a deep learning-based model, called Gated Spatial–Temporal Attention (GSTA), to optimize the OD travel time prediction. While many trip features are available, their relations and particular contributions to the output are usually unknown. To give our model the flexibility to select the most relevant features, we develop a feature selection module with an integration unit and a gating mechanism to pass or suppress the trip feature based on its contribution. To capture spatial–temporal dependencies and correlations in the short and long term, we propose a new pair-wise attention mechanism with spatial inference and temporal reasoning. In addition, we adapt and integrate multi-head attention to improve model performance in case of sophisticated dependencies in long term. Extensive experiments on two large taxi datasets in New York City, USA, and Chengdu, China demonstrate the superiority of our model in comparison with other models. [ABSTRACT FROM AUTHOR]