A numerical solution method of the incompressible Reynolds-Averaged Navier-Stokes equations is applied for calculating turbulent flows and performances of a marine propeller in open-water, four-quadrant conditions. Computed propeller flows of the model propeller P4381, for which the experimental data of the open-water performances exist, reveal complex viscous-flow characteristics including three-dimensional flow separations in various off-design conditions and also computed propeller thrusts and torques agree quite well with experimental data except some cases for which severe propeller cavitations occurred in the experiment.