Metallic foams as a filler in thin-walled structures can improve their crashworthiness characteristics. In this article, nonlinear parametric finite element simulations of FGF foam-filled conical tube are developed and the effect of various design parameters such as density grading, number of grading layers and the total mass of FGF tube on resulting mode shapes, specific energy absorption and initial peak load is investigated. Multi design optimization (MDO) technique and the geometrical average method, both are based on FE model are applied to maximize the specific energy absorption and minimize the impact peak force by estimating the best wall thickness and gradient exponential parameter "m" that controls the variation of foam density. The results obtained from the optimizations indicated that functionally graded foam material, with graded density, is a suitable candidate for enhancing the crashworthiness characteristics of the structure compared to uniform density foam.