Closed-cell stochastic foams are widely used in engineering field due to the excellent energy absorption capability. In this paper, the crushing response of three dimensional closed-cell foams is investigated under quasi-static and dynamic compression loading. Voronoi tessellation is employed to generate the mesoscale geometric models of closed-cell stochastic foams, and subsequently numerical analysis is carried out using LS-DYNA software. Results reveal that the plateau stress of Voronoi model under quasi-static compression linearly increases with the increase of relative density. In addition, the mechanical properties of Voronoi model under quasi-static and dynamic compression are related to a shear band collapse mode and a layer-wise collapse mode, respectively. The plateau stress and the densification strain under high-speed loading are higher than those under quasi-static and low-speed loading.