The catalytic conversion of carbon dioxide (CO2) into methanol, a valuable chemical product, has been investigated theoretically on a novel holmium (Ho)-doped Cu(211) surface by density functional theory (DFT) calculations. The possible key intermediates formed during the hydrogenation of CO2 and as well as their further hydrogenated species during the production of methanol are examined thermodynamically and kinetically by computational means. It is found that the adhesion of a Ho atom on the Cu(211) surface enhances the interaction of reactants, especially CO2 molecules, with the surface. This enhancement in the interaction energy, in turn, increases the catalytic activity of the Cu(211) surface. Unlike other Cu surfaces, the Ho-doped Cu(211) surface activates CO2 better than H-2 molecules. The reaction mechanism proceeds through the formation of formate (HCOO), dioxymehylene (H2COO), dissociation of H2COOH into H2CO and OH, and finally the hydrogenation of H2CO to H3COH. The addition of a Ho atom stabilizes the H2COO intermediate rather than the HCOOH intermediate. Among the various intermediates, the last hydrogenation step has the highest activation barrier (1.02 eV), which is followed by the formation of HCOO (0.96 eV) and H2COO (0.95 eV) surface species.