This paper presents a method to simulate unsteady viscous nonlinear waves by numerically solving Navier-Stokes equations. The equations were solved by a finite difference method with a free surface fitted coordinate system, which is regrided every time step. The time derivatives were approximated by a time splitting fractional step method. Second order central differences were used to discretize the viscous and pressure terms while the convection terms were discretized by a QUICK scheme. A cell centered stencil was used. In order to check the accuracy of the present scheme, the following test problems were solved numerically: (1) standing wave problems, (2) the propagation and reflection of a soliton, (3) piston-type wavemaker simulations, and (4) the wave generation by a moving topography. The computational results are compared to analytical results when available and good agreements were obtained. The present scheme was thus validated.