In this paper, a functionally graded foam model is proposed in order to improve upon the energy absorption characteristics offered by uniform foams. In this novel model, the characteristics of the foam (e.g. density) are varied through the thickness according to various gradient functions. The energy absorption ability of the novel foam is explored by performing finite element simulations of physical impact tests on flat specimens of the functionally graded foam materials. Energy absorbing capacity w.r.t. parameters including gradient functions, density difference, average density, and impact energy, is explored in detail. It is illustrated that the functionally graded foam is superior in energy absorption to the uniform foam and that convex gradients perform better than concave gradients. The performance of such foams can be improved more if the density difference is enlarged. These findings provide valuable suggestions in the design of high performance energy absorption polymeric foams.