The accurate prediction of ship trajectory has great significance in maritime transportation. Among all the prediction methods, multi-step prediction has received increasing attention because it can predict both time and position information in the future period. However, the existing methods are either complex or have low prediction accuracy. In order to overcome the limitations, a physical hypothesis is introduced to balance the complexity and the accuracy. The cubic spline interpolation and historical trajectories are used to realize it. The advantages of TPNet and LSTM are combined in the proposed method and four parts are involved: the AIS data preprocessing method, the solutions of destination point and support point, and the uncertainty analysis. The proposed method is not only easy to implement and suitable for real-time analysis, but also has a high prediction accuracy. The case study on a ferry ship in the Jiangsu section of the Yangtze River indicates the validity of the method. •Complex mapping relationships and large data requirements for multi-step prediction is solved.•A physical constraint is used in the construction of the model.•An automatic generation method of reference trajectory based on ship motion parameters is proposed.•The effectiveness of the method is verified by making predictions under four different navigation states.