ZnO is a wide bandgap semiconductor with the advantages of good stability, strong radiation resistance, and low cost. It has become a hot material in the field of photocatalysis, but it can only absorb purple light. Therefore, it is a valuable problem to study how to expand the response range of ZnO to visible light. Doping modification is a common method to solve this problem. In order to carry out the relevant research, the calculation in this paper are carried out by the CASTEP tool in Materials Studio software based on the first-principles of ultrasoft pseudopotential of density functional theory, the geometric structures of ZnO, Zn_0.875Pr_0.125O, ZnO_0.875N_0.125, Zn_0.875Pr_0.125O_0.875N_0.125, Zn_0.75Pr_0.25O_0.875N_0.125, Zn_0.625Pr_0.375O_0.875N_0.125 are constructed. All the models are based on the optimization of the geometry structure. By using the method of generalized gradient approximation plus U, we calculate the band structure, density of states, population, absorption spectra and dielectric functions of the models. The results show Co-doped system is easier to form than single-doped system, and the stability of the co-doped system increases first and then decreases with the increase of Pr concentration. The population ratio of the shortest Zn-O bond to the longest Zn-O bond in the same system increases first and then decreases with the impurity concentration, which shows that the doping of impurities has a great influence on the lattice distortion of the system, and the distortion is benefit for the separation of photogenerated hole-electron pairs. Therefore, the photocatalytic activity of the materials can be improved. Hybridization of N-2p and Pr-4f states destroys the integrity of crystals and forms crystal fields around impurity atoms, which results in splitting of energy levels and narrowing of bandgap. Compared with intrinsic ZnO, the static dielectric constant of all doped systems increases, especially the constant of Pr-N co-doped systems increases with the increase of doped Pr concentration, which indicates that the polarization ability of the co-doped systems increases with the increase of doped Pr atomic concentration. The main peaks of the dielectric function imaginary part of the doping systems move to the low energy region, and the absorption spectrums are red-shifted. As the concentration of impurity Pr atom increases, in the visible region, the absorption capacity of each co-doped system increases, their response range is enlarged in turn, showing the co-doping of N and Pr is benefit for improving the photocatalytic activity of ZnO.