To achieve space-air-ground-sea integrated communication networks for future sixth generation (6G) communications, unmanned aerial vehicle (UAV) communications applying to maritime scenarios serving as mobile base stations have recently attracted more attentions. The UAV-to-ship channel modeling is the fundamental for the system design, testing, and performance evaluation of UAV communication systems in maritime scenarios. In this paper, a novel non-stationary multi-mobility UAV-to-ship channel model is proposed, consisting of three kinds of components, i.e., the line-of-sight (LoS) component, the single-bounce (SB) components resulting from the fluctuation of sea water, and multi-bounce (MB) components introduced by the waveguide effect over the sea surface. In the proposed model, the UAV as the transmitter (Tx), the ship as the receiver (Rx), and the clusters between the Tx and Rx, can be seen as moving with arbitrary velocities and arbitrary directions. Then, some typical statistical properties of the proposed UAV-to-ship channel model, including the temporal autocorrelation function (ACF), spatial cross-correlation function (CCF), Doppler power spectrum density (PSD), delay PSD, angular PSD, stationary interval, and root mean square (RMS) delay spread, are derived and investigated. Finally, by comparing with the available measurement data, the accuracy of proposed channel model is validated.