Three-dimensional viscous flows around a single-rotation high-speed propeller are investigated by solving compressible Navier-Stokes equations. An implicit finite difference code based on a high accuracy TVD scheme with a Baldwin-Lomax model of turbulence has been developed and applied. Computations are successfully carried out at cruise and take-off conditions with particular emphasis on grid resolution effects. The solutions clearly capture a leading edge vortex as well as a shock wave so that physical characteristics of the flow field are made clear. Numerical results are compared with the experimental data. Computed surface flow patterns show good agreement with oil flow visualization results. The present results show that the Navier-Stokes approach is capable of accurately simulating viscous phenomena around the propeller while the Euler analysis cannot, and that the propeller flow field is unexpectedly complicated because of the thin, highly swept blade.