Foam-filled tubes have recently gained attention due to their excellent energy absorption capacity. In order to improve the crashworthiness of foam-filled tubes, the energy absorption characteristics of two kinds of functionally lateral graded foam-filled tubes (FLGFTs) are investigated in this paper. Based on the numerical results, it is found that each of the two kinds of FLGFTs has more excellent energy absorption capacity than the ordinary uniform foam-filled tube (UFT) with the same weight. In addition, it can also be found that the gradient exponential parameter m which controls the variation of foam density gives rise to significant effects on the crashworthiness of FLGFTs. Thus, in order to seek for the optimal gradient exponential parameter, the two kinds of FLGFTs are optimized by multiobjective particle swarm optimization (MOPSO) algorithm, aiming to achieve the maximum specific energy absorption (SEA) and the minimum peak crushing force (PCF). During the process of multiobjective optimization design, the 7th-order polynomial functions of SEA and PCF are established and found to be accurate enough for engineering design. The results obtained by optimizations further indicate that the optimal FLGFT performs more excellent energy absorption characteristics than ordinary UFT. The optimization design data is a good guidance for the crashworthiness design of FLGFTs.