The electronic structure of pure N-doped and In-N codoped wurtzite ZnO has been calculated by using first-principles ultra-soft pseudo-potential approach of the plane wave based upon the density functional theory，and the structure change，bandstructure，density of states，difference charge density and the influence of In-N codoped wurtzite ZnO by H atom were studied. The calculation results revealed that N-doped wurtzite ZnO caused formation of deep N acceptor levels in the band gap and the carriers (hole) were localized near the top of the valence band. But the codoping calculation revealed that the acceptor level shifted toward the lower-energy region and shallow acceptor level were fomed，which was broadened and showed delocalizing characters, owing to which the concentration of impurities and the stability of the system were enhanced. Our conclusions accord with the results of experiments, which confirms the fact that In-N codoping in wurtzite ZnO helps the formation of p-type ZnO. In addition, it was also pointed out that the presence of H atom reduces the efficiency of doping markelly，which should be avoided as much as possible.