Excessive acceleration is one of the stability failure modes involving large-amplitude roll of a ship. The applicabilityof the vulnerability criteria of excessive acceleration for a ship with moonpool is compared and analyzed. The influence of the roll damping of the moonpool on the assessment of the ship long-term failure probability is studied by comparing the ship lateral acceleration and the long-term failure probability that are calculated by using the roll damping coefficients of different initial roll angles. The catenary mooring model is used to constrain the sway of the ship, and the six degrees of freedom (6-DoF) of the ship with moonpool in beam waves is simulated by using the Realizable turbulence model. The feasibility of using computational fluid dynamics (CFD) method to directly evaluate the stability of the ship with moonpool under excessive acceleration is validated by comparing with the experimental results. The results show that the Level 1 vulnerability criterion is not suitable for the sample ship, whereas for the sample ship with moonpool, the equivalent linear roll damping coefficient from the free roll attenuation test with an initial roll angle of 10° is recommended to be used in the Level 2 vulnerability criterion of the excessive acceleration. The accuracy of the direct numerical simulation of the excessive acceleration based on CFD method is acceptable for the ships with moonpool.