Foam-filled thin-walled structure has been widely used in vehicle engineering due to its highly efficient energy absorption capacity and lightweight. Unlike the existing foam-filled thin-walled structures, a new foam-filled structure, i.e., functionally graded foam-filled graded-thickness tube (FGFGT), which had graded foam density along the transverse direction and graded wall thickness along the longitudinal direction, was first studied in this paper. Two FGFGTs with different gradient distributions subjected to lateral impact were investigated using nonlinear finite element code through LS-DYNA. According to the parametric sensitivity analysis, we found that the two design parameters n(1) and n(2), which controlled the gradient distributions of the foam density and the tube wall thickness, significantly affected the crashworthiness of the two FGFGTs. In order to seek for the optimal design parameters, two FGFGTs were both optimized using a metamodel-based multi-objective optimization method which employed the Kriging modeling technique as well as the nondominated sorting genetic algorithm II. In the optimization process, we aimed to improve the specific energy absorption and to reduce the peak crushing force simultaneously. The optimization results showed that the FGFGT had even better crashworthiness than the traditional uniform foam-filled tube with the same weight. Moreover, the graded wall thickness and graded foam density can make the design of the FGFGT flexible. Due to these advantages, the FGFGT was an excellent energy absorber and had potential use as the side impact absorber in vehicle body.