Ship motion forecasting is of great significance to assist ship navigation and ensure ship operation. However, due to the coupling influence of wind, waves, currents and other factors, the ship motion has a strong time variation, which brings great challenges to the improvement of the ship motion forecasting accuracy. This paper proposes a novel approach for ship motion forecasting. Firstly, Fourier Transform (FT) is used for data pre-processing to deal with the data noise. Secondly, the Bi-LSTM is applied to simulate the nonlinear dynamical system of ship motion, and the Dropout mechanism and l2 regularization method are used to improve the generalization performance of the network, and a novel ship motion prediction model (FRB model) is constructed. Thirdly, in view of the inherent defects of Whale Optimization Algorithm (WOA), based on chaotic mapping and quantum computing, a new Chaotic Quantum Adaptive Whale Optimization Algorithm (CQAWOA) is proposed to construct a new ship motion forecasting approach, namely FRB&CQAWOA. Finally, based on the measured pitch and roll data of ship, the feasibility and superiority of the established FRB model and the proposed CQAWOA are tested. The test results indicate that the proposed model have better prediction accuracy than other algorithms selected in this paper.