In order to enhance the load-carrying and energy-absorbing capacity of the energy-absorbing structure, a new energy-absorbing mode of a metal foam-filled sandwich circular tube (MFSC-Tube) expanded by a conical–cylindrical die under axial compression is designed. An analytical model of expansion of the MFSC-Tube under axial compression is established, considering the bending, stretching, and strain hardening of inner and outer tubes as well as compression of the metal foam core. Subsequently, finite element calculations are performed. Both analytical solutions and deformation modes agree well with the finite element calculation results, which proves the validity of the analytical model. The effects of material and geometrical parameters on the expansion of MFSC-Tubes are considered in detail based on the proposed analytical model. It is found that the load-carrying and energy-absorbing capacity of the expansion of the MFSC-Tube can be enhanced by adjusting such parameters as the ratio of the foam thickness to the wall thickness of the metal circular tube and the semi-angle of the die. Last but not least, the specific energy absorption (SEA) of the MFSC-Tube under expansion is significantly improved compared with that of hollow tubes under expansion.