A Cartesian grid method with CIP (Constraint Interpolation Profile ) based flow solver has been developed and applied to many strongly nonlinear free surface problems. In this paper we present a research on applying the method to predict nonlinear wave loads on a container ship, which is advancing at a constant forward speed in regular waves with large amplitudes. Numerical computations are carried out on a head sea case and a bow sea case. The computed frequency response characteristics for the ship motions and the wave loads including vertical bending moments on the cross-sections and hydrodynamic pressures on the hull, are compared to a model test result and the result obtained by two potential flow based numerical methods. The nonlinear features of the numerical results are discussed.