The development of highly efficient electrocatalysts and understanding the reaction mechanisms during the discharge and charge is essential for the designs of advanced Li-CO2 batteries, but still remains a great challenge. Herein, by using first-principles density functional theory calculations, we systematically investigated the 21 types dual-atom catalysts (DACs), including homonuclear and heteronuclear transition-metal sites (M1M2NC, M1 and M2 are one of the Mo, Mn, Fe, Co, Ni, Cu elements), and studied the possible reaction mechanisms for Li-CO2 batteries. Through the comparison of the adsorption energy and the orbital interactions, we have verified that the multi-orbital interactions between dyz, dxz, dz2 orbitals of TMs and the hybrid 2p orbitals of CO2 result in superior bonding interaction of CO2 on DACs. Furthermore, based on these orbital interactions, we found that the DACs with lower d center preferentially have higher CO2 activation capability, and therefore defined the relationship between adsorption energies and d band centers. Accordingly, we confirmed that the two linear relationships between the CO2 and Li2CO2 adsorption energies and the limiting potential, which can accurately describe the overall performances toward Li-CO2 evolution on the DACs. The correlations among CO2 activation, orbital interactions and the catalytic performances obtained in this work pave a way for rational design of DACs for improving the efficiency of Li-CO2 batteries.