The Moving particle semi-implicit (MPS) method is a widely used approach to simulate the violent interactions between dam break flow and downstream structures. However, most of these simulations involved fixed downstream structures and rarely considered floating objects. In this study, a modified MPS method, named MPS-SP-MG-PS method, is proposed to simulate violent interactions between dam break flow and a floating box. The proposed method includes below modifications: (1) the MPS-SP scheme with a split-pressure Poisson equation; (2) a modified space potential particle (SPP) scheme; and (3) a mixed pressure gradient and a novel particle shifting (PS) technique. Two cases are simulated, one considers heave motion only, and another considers both heave and pitch. Slamming, wave-on-deck and severe motions are involved in the cases. In order to evaluate the effect of these modifications, several numerical models with different combinations of the modifications are tested as well. Numerical results demonstrate the enhancement on stability and accuracy by these modifications: the MPS-SP scheme ensures the stability of heave motion at the initial stage; the modified SPP scheme maintains reasonable distance between free surface particles; and the combination of the mixed pressure gradient and the novel PS technique shows its accuracy in estimating box motions. Furthermore, the numerical results from the MPS-SP-MG-PS method are well consistent with experimental and existing numerical results in terms of box motions, surface elevations, fluid profiles, and slamming pressure. This indicates that the MPS-SP-MG-PS method is suitable for simulating violent interactions between dam break flow and floating structures.