Ship trajectory prediction is a core technology for intelligent shipping, yet existing models suffer from high computational costs, inadequate modeling of global spatio-temporal dependencies, and lack of privacy protection when processing long-sequence data. To address these challenges, this paper proposes a ship trajectory prediction and privacy-preserving scheme based on Mamba-Transformer fusion. The scheme innovatively designs a dual-path parallel architecture in the trajectory prediction module, efficiently capturing long-range temporal dependencies through the linear scaling capability of the Mamba branch while leveraging the powerful global modeling capability of the Transformer branch to extract macroscopic trajectory patterns. Deep fusion is achieved through a hierarchical multi-head attention module designed in this work, thereby effectively capturing both local navigation details and global trajectory patterns simultaneously. Furthermore, recognizing that real-time trajectory prediction poses higher privacy leakage risks compared to delayed publication, the proposed scheme introduces a differential privacy mechanism at the model output layer, with a time-decay-based privacy budget allocation strategy that significantly enhances the utility of published trajectories under privacy protection. Experimental results on the Danish maritime dataset demonstrate that the proposed scheme achieves substantial improvements in ship trajectory prediction accuracy over existing methods while providing rigorous privacy guarantees for high-precision predictions through a flexible differential privacy mechanism.