A finite-volume method is newly developed and applied to a flow about a ship. It employed an explicit time-marching procedure with the subgrid scale turbulence model without any wall function on the body surface. The curvilinear grid system is fitted not only the hull surface but also to the free-surface which is deformed with respect to the wave motion. Simulations are carried out for the HSVA tanker with and without free-surface as well as the Wigley's hull with free-surface. The comparisons between simulated and measured results show quite excellent agreement in the waves, pressure and wake distributions. The simulated results reveal the systematic formation of the longitudinal vortices, the flow separation from the hull surface, the generation of vortices in the vicinity of the free-surface and the complicated interaction of vortices near the after end of a ship.