The plunging wave impacts on a box-shape structure are investigated experimentally and numerically, focusing on three typical scenarios with distinct features, i.e. the wave impact occurs after, upon and before wave breaking. In the experiments, the plunging wave is generated by a piston-type wave maker whose motion is governed by the focused wave theory. The fixed box-shape structure mimics the offshore platform structures. Measured are the wave elevations at typical positions, the wave impact pressures on the front and bottom (violent impact is very likely to occur) of the platform, and the wave profiles of the transient wave impact process. The experiment identifies the pressure maximums both on the front and bottom walls under three different wave impacts. The pressure oscillation along the front wall is observed and analyzed by examining the evolution of air cavity. The experimental parameters and dimensions including the actual wave maker motion signal was inputted into the numerical model to reproduce the same case. Numerical simulations using an improved immersed boundary method are compared with the experimental results with roughly good agreements being achieved. Besides, numerical pressure distributions along the front and bottom walls are presented to find different modes of wave impact. Finally, the maximal pressures on the front wall of the box-shape structure are normalized by two approaches, and compared with the documented maximal pressure ranges.