We report the first high-order eddy-resolving simulation of flow over a marine propeller using a recently developed high-order sliding-mesh method. This method employs the flux reconstruction framework and a new dynamic curved mortar approach to handle the complex rotating geometries. For a wide range of working conditions, it is validated to predict the loads very accurately against experiments. The method’s low-dissipation characteristic has allowed the capturing of a broad spectrum of turbulence structures for very long distances even on a very coarse grid. Comparison with a previous low-order simulation is also carried out to show the low-dissipation advantage of the present simulations. From detailed load analysis, the major loads and their distributions and time and frequency scales are identified. Visualizations of the instantaneous, phase-averaged, and time-averaged flow fields have revealed the processes of tip vortex formation, major vortex evolutions, and flow instability developments at different working conditions. The effects of different fairwaters on the propeller’s overall performance are also quantitatively assessed.