Metal-graphene system was taken as the research object. Density functional theory (DFT), combined with local density approximation (LDA) and PWC functional, was employed to study the changes in the geometry structure, energy, charge distribution and density of states (DOS) of the systems before and after absorption of CO₂ on them. The results show that the electrons are transferred from the M-graphene system to CO₂, which is eventually activated by negative charge. The Cu-G system is most effective to activate CO₂ in these three complexes. The bond length of CO₂ increases by 6 and 14 pm, respectively, and the bond angle of O—C—O decreases to 122°. Furthermore, the first ionization energy and electron affinity of metal clusters and graphene play a decisive role in the electron transfer. Compared with the first ionization energy of graphene, the larger the electron affinity of metal clusters, the more the electrons transferred from graphene to metal cluster.