A deeper understanding of the uniaxial compression damage behavior and its microscopic mechanisms in closed-cell Polyurethane foam (PUF) at higher strains would be the first step to comprehend its energy absorption behavior in application. A physical-based micro-structure of the PUF model, therefore, is a crucial precondition in the prediction of the material property. A highly efficient physical-based model with adapted periodic boundary conditions (PBCs) is developed to simulate the mechanical behavior of the rigid closed-cell foam using 100 cells, much less than that mentioned in the literature (800 cells). The microstructure characteristics of PUF have been obtained by scanning electron microscopy (SEM), including the cell size distribution, the wall thickness, the cell aspect ratio, etc. Using these parameters, a periodic representative volume elements (RVEs) model based on the Laguerre tessellation with centroidal constraint and capacity constraint (LTCCC) has been proposed. The centroidal constraint and capacity constraint on the LTCCC has a sound physical meaning that the volume distribution of the cells in the RVEs model obtained by the iterations of the weights of the seed points can be precisely matched to that measured using the SEM. Meanwhile, the features of the RVEs model, including the number of the faces per cell and the number of the edges per face, also match those of the real foam. The anisotropic compressive behavior of the PUF is predicted and well validated using the experimental results. The quasi-static crushing progress of the cells as well as the struts is detailed discussed using the proposed model to reproduce the layer-wise collapse phenomena and reveal the reasons that cause the different crushing behavior in axial direction and perpendicular to the axis direction.