The electronic structures and optical properties of intrinsic, Cu, Co doped and Cu-Co codoped ZnO compounds are calculated using first-principles plane-wave ultrasoft pseudopotential method based on the the density functional theory. The results show that the conductivity of ZnO can be improved by doping Cu and Co because of the increase of the carrier concentration under the order of magnitude of doping concentration in this paper. Cu-Co codoping leads to the degeneration and makes ZnO metallic. Thses three kinds of dopings can cause light absorption enhancement phenomenon in the visible and near ultrasoft regions, in which Cu-Co codoping greatly increases the absorption of solar light due to the synergistic effect between Cu ions and Co ions, which can be used to prepare the high efficiency solar cells.