The velocity of ocean currents significantly affects the trajectory prediction of ocean drifters and the safe navigation of intelligent vessels. Currently, most ocean current predictions focus on time-based forecasts at specific fixed points. In this study, deep learning based on the flow field prediction model (CNNs–MHA–BiLSTMs) is proposed, which predicts the changes in ocean currents by learning from historical flow fields. Unlike conventional models that focus on single-point current velocity data, the CNNs–MHA–BiLSTMs model focuses on the ocean surface current information within a specific area. The CNNs–MHA–BiLSTMs model integrates multiple convolutional neural networks (CNNs) in parallel, multi-head attention (MHA), and bidirectional long short-term memory networks (BiLSTMs). The model demonstrated exceptional modelling capabilities in handling spatiotemporal features. The proposed model was validated by comparing its predictions with those predicted by the MIKE21 flow model of the ocean area within proximity to Dalian Port (which used a commercial numerical model), as well as those predicted by other deep learning algorithms. The results showed that the model offers significant advantages and efficiency in simulating and predicting ocean surface currents. Moreover, the accuracy of regional flow field prediction improved with an increase in the number of sampling points used for training. The proposed CNNs–MHA–BiLSTMs model can provide theoretical support for maritime search and rescue, the control or path planning of Unmanned Surface Vehicles (USVs), as well as protecting offshore structures in the future.