Due to the strong coupling characteristic of the hovercraft during the movement and its own structural specificity, the hovercraft has poor maneuverability and is prone to danger during the navigation. In order to predict the attitude of the hovercraft and improve the hovercraft safety, this paper proposes a novel compound prediction model based on grey theory and improved Elman neural network. Grey prediction has the structural advantages of low number of original data and less effective information, but its processing ability to non-linear systems is weak. Elman neural network has the function of self-learning and self-organizing to solve the non-linear system. By combining the two models, a non-linear system with less raw data can be processed. The model prediction results are determined by the individual prediction results and the weighted weight values of the model. Different weight coefficient ratios are assigned to different models to jointly obtain the results of the final compound prediction model. The simulation results show that this kind of compound prediction method has higher prediction accuracy with smaller predictive error in the hovercraft motion prediction application.