The excessive acceleration is one of five stability failure modes for intact stability being discussed at IMO. The excessive acceleration usually occurs in shallow draft state, under which the ship is prone to large nonlinear rolling motion. Therefore, the accurate prediction and evaluation of the acceleration response are required in ship intact stability analysis. This paper proposes a 5-DOF model in time domain to calculate the nonlinear acceleration response of a large container ship. The nonlinear restoring force and wave exciting forces (F-K force) are calculated through pressure integration on instantaneous wetted surfaces. A model test has been carried out to verify the prediction method of ship nonlinear acceleration response in the regular and irregular waves. It turns out the ship nonlinear acceleration response in regular and irregular waves obtained by the nonlinear time domain simulation agrees well with the experimental results. The vulnerability criteria for excessive acceleration are also validated by numerical and experimental results. In addition, the influence factor of ship lateral acceleration is studied. The results show that the prediction accuracy of 5-DOF model is acceptable. However, the accuracy needs to be improved for the condition of short wavelength. The influence of angular velocity can be ignored.