This paper is focused on the in-plane crushing of two-dimensional (2D) porous structures with a special attention on the effect of functionally graded (FG) porosities. The dynamic response and energy absorption of closed-cell metal foams with different porosity distributions are investigated by using finite element (FE) analysis. Two symmetric, two asymmetric and one uniform distributions of internal pores along the impact direction are constructed with Voronoi tessellation. The proposed porous structure is crushed under the impact of a rigid panel with a constant velocity. The deformation of cell walls is simulated using a plastic kinematic material model. The erosion criteria and hourglass control are applied to ensure the accuracy of numerical results, which are validated against the experimental data from open literature. The effects of varying parameters on the energy absorption, deformation pattern, and stress-strain curve of the FG porous structure are discussed. The dynamic response is found to be influenced by different random cell geometries, porosity gradients, cell wall thicknesses, internal pore numbers, and impact velocities. The effective way to improve the energy absorption capability of the porous structure under a constant-velocity impact is proposed, shedding new insights into the deformation mechanism of the FG porous structure for engineering design. Display omitted •The porosity distribution of porous structures has a significant influence on the dynamic response.•The energy absorption under high-velocity impacting can be improved with the proposed graded porosity distribution.•The absorbed energy of porous structures increases with the increasing impact velocity.•The densification of cell walls tends to localize near the impact end under high impact velocities.