A numerical code based on the moving particle semi-implicit (MPS) method has been developed for time-domain simulations of extreme motions of a floating body. The MPS method is a gridless CFD technique that can treat incompressible flow with perfect conservation of mass and no numerical diffusion. The code can be applied to extreme motions of solid boundaries and large deformation of the free surface without numerical difficulties. There is no inconsistency even in handling the fragmentation and reunite of fluid. In this paper, an overview of the MPS method and details of the treatment in floating-body simulations are explained. Simulations of capsizing with flooding and porpoising with advance velocity are demonstrated as an application of the developed code.