The Cu/CeO.sub.2-nanopolyhedrals and pure Cu/CeO.sub.2-nanorods with different sizes were synthesized for CO.sub.2 hydrogenation to methanol. With increasing the percentage composition of CeO.sub.2 nanorods, the surface concentrations of Cu.sup.+, Ce.sup.3+ and oxygen vacancies were gradually enhanced. However, the amount of surface Cu.sup.+ species and oxygen vacancies would be decreased instead if the size of pure CeO.sub.2 nanorods was too large. The variation tendency of catalytic performance for CO.sub.2 hydrogenation to methanol was well consistent with that of Cu.sup.+ species and oxygen vacancies. Cu/CeO.sub.2 nanorods with small size exhibited the strongest interaction in Cu-CeO.sub.2 interface and the highest methanol production activity among all Cu/CeO.sub.2 nano-catalysts. The small size of CeO.sub.2-nanorods obtained at NaOH concentration of 10 mol/L, hydrothermal temperature of 80 °C and hydrothermal time of 24 h showed the best catalytic performance (X.sub.CO2 = 5.8%, S.sub.CH3OH = 92.0%, Y.sub.CH3OH = 5.3%) at 280 °C and 3 MPa. The stronger interaction accelerated the charge transfer between CuO.sub.x species and CeO.sub.2 nanorods, which produced the larger amount of surface Cu.sup.+ species and oxygen vacancies. The synergistic effect between reduced Cu species and oxygen vacancies improved methanol selectivity and was responsible for CO.sub.2 hydrogenation to methanol.