The vessel trajectory prediction plays a vital role in guaranteeing traffic safety for unmanned surface vehicles and autonomous surface vessels. By leveraging advanced satellite communication technology, AIS provides massive vessel trajectories, significantly enhancing maritime safety and decision-making. This research proposes a spatio-temporal multi-graph transformer network (ST-MGT), aiming to predict multiple vessel trajectories simultaneously. This innovative model amalgamates the capabilities of graph convolutional networks (GCNs) and transformer models to proficiently address the spatial and temporal interactions amongst vessels. The ST-MGT is comprised of three crucial layers. The temporal transformer layer employs sophisticated temporal transformer and memory mechanisms to discern the intricate temporal correlations between vessel movements. The spatial multi-graph transformer layer constructs a comprehensive multi-graph representation to illuminate spatial correlations between vessels. It incorporates a spatial graph convolutional network and transformer to meticulously understand and interpret the diverse and complex spatial interactions amongst varying vessels. Lastly, the ξ-Regularized LSTM (RegLSTM) layer is implemented for predicting vessel trajectories accurately, based on the unraveled spatio-temporal patterns. Extensive and meticulous experiments reveal that our proposed ST-MGT method transcends other state-of-the-art prediction models in robustness and accuracy. The model’s capability to facilitate multi-vessel and multi-step prediction showcases its immense potential and adaptability in intricate and multifaceted navigation environments, underscoring its practical applicability and significance in enhancing maritime navigational safety.