The band structure, the density of states and optical absorption properties of Cu-doped ZnO were studied by the first-principles generalized gradient approximation plane-wave pseudopotential method based on density functional theory. For the Zn_1-xCu_xO (x = 0, x = 0.0278, x = 0.0417) original structure, geometric optimization and energy calculations were performed and compared with experimental results. With increasing Cu concentration, the band gap of the Zn₁-_xCu_xO decreased due to the shift of the conduction band. Since the impurity level was introduced after Cu doping, the conduction band was moved downwards. Additionally, it was shown that the insertion of a Cu atom leads to a red shift of the optical absorption edge, which was consistent with the experimental results.