The study of Cu on ZnO surfaces is a topic of ongoing research due to the importance of Cu as a promoter in the low-temperature synthesis of methanol, the water-gas shift process, and methanol steam reforming. The role of ZnO in supporting the stabilization of the Cu atoms and promoting the CO2 hydrogenation reaction is multifaceted and involves a range of physical and chemical factors. In this work, we used density functional theory (DFT) calculations to investigate the Cu adsorption on ZnO surfaces on different sites. Bader charge analysis, adsorption energy, and phonon inelastic neutron scattering (INS) associated with most stable systems were calculated and compared with previous theoretical and experimental results. We found that atomic Cu adsorption on hollow site of ZnO(111) is the most stable site and most favorable site for Cu adsorption comparing to other ZnO surfaces. This is due to the strong metal-oxygen interaction between Cu and the ZnO surface. The results suggest that the Cu/ZnO catalyst with Cu atoms at hollow site is most likely to be active for CO2 hydrogenation. We concluded that further studies are needed to investigate the catalytic activity of this catalyst under realistic reaction conditions with realistic models of Cu supported on ZnO.