Using the ASED-MO (Atom Superposition and Electron Delocalization-Molecular Orbital) theory, we investigated carbon formation and carbon hydrogenation for $CO_2$ methanation on the Ni (111) surface. For carbon formation mechanism, we calculated the following activation energies, 1.27 eV for $CO_2$ dissociation, 2.97 eV for the CO, 1.93 eV for 2CO dissociation, respectively. For carbon methanation mechanism, we also calculated the following activation energies, 0.72 eV for methylidyne, 0.52 eV for methylene and 0.50 eV for methane, respectively. We found that the calculated activation energy of CO dissociation is higher than that of 2CO dissociation on the clean surface and base on these results that the CO dissociation step are the ratedetermining of the process. The C-H bond lengths of $CH_4$ the intermediate complex are 1.21 $AA$, 1.31 $AA$ for the C${cdot}{cdot}{cdot}H_{(1)}$, and 2.82 $AA$ for the height, with angles of 105${^{circ}}$ for ∠ $H_{(1)}$CH and 98${^{circ}}$ for $H_{(1)} CH _{(1)}$.