For free surface flow computations with an unstructured grid, an interface capturing method using a level set function which is the signed distance from the interface has been developed. The level set equation is discretized by the finite volume method on an unstructured grid with the Euler backward scheme for the time integration. This procedure is coupled with the unstructured Navier-Stokes solver discretized in the similar manner. Due to the special extrapolation procedure to satisfy free surface boundary conditions, only the water portion of a flow domain needs to be solved. Numerical results for free surface flows around a hydrofoil and around a ship demonstrate the capability of the present solver.