Based on the first-principles calculations with density functional theory, the formation energy and electronic structure of (S, Cu) co-doped ZnO has been investigated, where the doping cases including related defects for Cu mono-doped, S-Cu co-doped, and S-2Cu co-doped ZnO are studied. The calculated results show that the formation energy of S-2Cu complex is lower than that of S-Cu complex under the O-rich condition. From the electronic structure, S-2Cu complex forms a peak of impurity state at the top of valence band. It was further found that heavy doping of Cu, not only enhances the acceptor concentration, but also leads to shallower acceptor energy level. Therefore, we concluded that S-2Cu complex is suitable for yielding better p-type conductivity in ZnO. The results are in good agreement with the experiment results.