Each vessel has its own way of sailing in the port region. Any autonomous vessel navigating such a scene should be able to predict the trajectories of surrounding ships and adjust its behaviour to avoid a collision. In this paper, combined with the sequence prediction method, a Long Short-Term Memory (LSTM) model is proposed to predict the trajectories of the vessels. The ground-truth Automatic Identification System (AIS) data in the port of Tianjin, China are used to train and test the proposed model. The experimental results prove that our model can predict ship trajectories accurately, and it is applicable to the autonomous navigation system.