Excessive acceleration is one of the stability failure modes involving large roll motion of ships. The overset method is applied to solve the six degrees-of-freedom motion of the ship with moonpool in beam waves. Based on a computational fluid dynamics (CFD) method, the improved method of considering the roll damping of square moonpool is proposed. The improved method of considering moonpool damping is used in vulnerability assessment for excessive acceleration. The comparative analysis of the level 1 and level 2 vulnerability assessment of the excessive acceleration of a ship with moonpool is completed. The influence of moonpool on the vulnerability assessment of excessive acceleration is studied by comparing the model test results. The results show that the main factor affecting the estimation accuracy of lateral acceleration of the ship is the accuracy of roll amplitude calculation. The existence of moonpool will reduce the roll damping coefficient of the ship. The improved methods proposed in this paper can effectively improve the estimation of lateral acceleration of ships with moonpool in the level 1 vulnerability criteria and increase the safety margin in the level 2 vulnerability assessment. In the direct stability assessment, the CFD method can simulate the large-amplitude roll motion of the ship with moonpool and bilge keels, and can capture the strong nonlinear phenomena.