A numerical method for the solution of the Navier-Stokes equations in the case of a moving body is presented. The fluid is assumed to be incompressible. A cell-based finite volume method for unstructured grids is applied as the numerical method. The method is applied to problems of flow around a floating body. A floating body with or without bilge keels undergoing roll motions with different roll angles are taken as model case. Evaluation of hydrodynamic coefficients due to viscous forces is conducted. The numerical results show that the roll-damping coefficients obtained by using the Navier-Stokes solver are larger than the radiation damping coefficients evaluated by the linear potential theory due to viscous and vortex effect.