Understanding the mechanism and selectivity of CO₂ catalytic conversion by H₂ on a specific catalyst is of great significance in the context of renewable energy storage from a societal and technological point of view. In this paper, based on the density functional theory calculations, the possible reaction networks of CO₂ hydrogenation on the Ni₁₃ cluster are studied systematically. The adsorption energies of the reaction intermediates at various possible adsorption sites, the reaction energies and the activation energies of each elementary reaction are calculated. The results suggest that the adsorption properties of the CO₂ and the intermediates on the Ni₁₃ cluster are different from the specific crystal plane such as Ni(111) surface, and the intermediates are highly activated on the Ni₁₃ surface. The most advantageous pathways for the production of HCOOH, CH₃OH, and CH₄ are determined, and the activation barrier of the corresponding rate-determining step is 1.63 eV, 1.55 eV, and 1.55 eV, respectively. This indicates that the Ni₁₃ cluster has higher activity towards CO₂ catalytic conversion compared with other catalysts such as Cu(111), Ni(111), and Pt/Ni(111) surface. Furthermore, the H₃CO* hydrogenation or the dissociation is demonstrated to be the crucial step in determining the selectivity for CH₃OH and CH₄.