Abstract: A method was developed to calculate ship＇s roll motion due to parametric and forced excitation. The differential equation of ship＇s parametrically and forcedly excited roll motion was established,taking the metacentric height GM-variation as a random parametrical excitation and the wave moment as the random forced excitation. The random parametrical excitation was calculated considering the hull form, pitch, heave and motions of the quartering waves, The responses of roll motion were obtained for the ship by different significant wave heights, ship speeds, heading angles and wave lengths, The results indicate that this approximation can be used to calculate the ship＇ s roll motion due to parametrical and forced excitation,and reveal the important effect of the random quartering wave on the ship rolling and capsizing.