When forecasting ship movements, the random errors of the inertial navigation system (INS) seriously affect the accuracy of general prediction methods. In actual measurement, the main causes of the random errors are electrostatic bias and micro-electric disturbance. In response to this problem, a novel type of dual-pass Long Short-Term Memory (LSTM) neural network architecture is developed, on the basis of regular LSTM neural network. In the designed dual-pass LSTM neural network, the random drift and the noise residual of the INS are regarded as a autoregressive moving average (ARMA) and generalized autoregressive conditional heteroskedasticity (GARCH) model. Through dual-pass layers, the prediction of drift and the correction of residual errors are realized respectively in the same time. The simulation of ship heave motion was carried out on the ship motion simulation platform, and the real-time datas which are measured by the INS are inputted to the trained dual-pass LSTM netural network. The experiment proved that, when training the same source datas offline, the average Root Mean Squared Error (RMSE) percentage of conventional LSTM network was 3.94%, but when training different source datas or training online, the prediction accuracy obvious decline. In contrast, the average RMSE percentage of the dual-pass LSTM neural network was 1.05% when training offline and 1.12% when training online. Compared with conventional LSTM networks, the dual-pass LSTM network is more targeted and has better adaptability in the field of ship-motion prediction, and this network restores the motion prediction to the actual trajectory of a ship more accurately. INDEX TERMS Dual-pass LSTM neural network, generalized autoregressive conditional heteroskedasticity (GARCH) model, inertial navigation system (INS).