Green water load is an important parameter to be considered in designing a modern ship or offshore structures like FPSO and FSRU. In this research, a numerical simulation method for green water phenomenon is introduced. The Navier-Stokes equations and the continuity equation are used as governing equations. The equations are calculated using Finite Difference Method(FDM) in rectangular staggered grid system. To increase the numerical accuracy near the body, the Cartesian cut cell method is employed. The nonlinear free-surface during green water incident is defined by Marker-density method. The green waters on a box in regular waves are simulated. The simulation results are compared with other experimental and computational results for verification. To check the applicability to moving ship, the green water of the ship which is towed by uniform force in regular wave, is simulated. The ship is set free to heave and to surge.