The stability, electronic structure and optical properties of ZnO with Cu/Ag doped and Cu-Ag codoped were studied by first-principles method. Formation energies of CuZn2 and CuZn1-CuZn3 are close to 0.0 eV, and negative for CuZn1-CuZn2, which indicates that Cu doped is effortless and tends to gather. The value for AgZn2 is 2.5 eV, and higher than 4.5 eV for AgZn1-AgZn2 and AgZn1-AgZn3. It’s difficult for Ag doping with higher concentration. Formation energies of CuZn1-AgZn2 and CuZn1-AgZn3 are close to that of AgZn2. The Cu3d and O2p states have obvious hybridization in models of CuZn2, CuZn1-CuZn2 and CuZn1-CuZn3, the top of valence band is mainly occupied by Cu3d states. The hybridization between Ag4d and O2p states for AgZn2, AgZn1-AgZn2 and AgZn1-AgZn3 models is weaker, the top of valence band is mainly occupied by O2p states. For CuZn1-AgZn2 and CuZn1-AgZn3 models, although Cu3d states hybridize with O2p states, the top of valence band is mainly occupied by O2p states. Cu/Ag doped and Cu-Ag codoped lead Zn4s states downward significantly, which reduces the band gap of above models. They influence the electronic structure of ZnO near the band gap mainly. The modified ability of Cu-Ag codoped to ZnO electronic structure is between Cu/Ag doped ZnO. The absorption edges of above models have obvious red-shift, which realizes the visible light absorption for ZnO. The ultraviolet light absorption also is higher than pure ZnO in the range of 3.10-3.90 eV. Cu/Ag doped and Cu-Ag codoped improves the photocatalytic activity of ZnO. According to formation energy analysis, the models with higher photocatalysis under different doping are CuZn1-CuZn2, AgZn2 and CuZn1-AgZn2.