The geometric structure，band structure and density of state of pure and N-Ga，2N-Ga codoped wurtzite ZnO have been investigated by first-principles ultrasoft pseudopotential method in the generalized gradient approximation. The calculation results show that the codoped structure N-Ga has better stability. Our work indicates that，the carrier concentration is increased in the 2N-Ga codoped configuration where the delocalized features are obvious，and this structure is more in favor of the formation of p-type ZnO.