The prediction of ship motion is significant for offshore activities, as it can provide helpful early warning information and improve the motion compensation system. In this study, we apply the reservoir computing (RC) model to predict the dynamic motions of a ship sailing in irregular waves, comparing it with the long short-term memory (LSTM), bidirectional LSTM (Bi-LSTM), and gated recurrent unit (GRU) networks. The model tests are carried out in a towing tank to generate the datasets for training and testing the machine learning models. First, we explore the performance of machine learning models trained solely on motion data. It is found that the RC model outperforms the other networks in both accuracy and efficiency for predicting ship motions. Besides, we investigate the performance of the RC model trained using the historical motion and wave elevation data. It is shown that, compared with the RC model trained solely on motion data, the RC model trained on the motion and wave elevation data can significantly improve the motion prediction accuracy. This study validates the effectiveness and efficiency of the RC model in ship motion prediction during sailing and highlights the utility of wave elevation data in enhancing the RC model’s prediction accuracy.