The crystal structure, density of states and electronic structures of Te-N doped ZnO are investigated from the first-principles pseudo-potential approach based on density functional theory. It is found that the incorporation of N into ZnO induces contraction of lattice, while Te incorporation will cause expansion of lattice. Thus, the co-doping of both Te and N is conducible to the incorporation of N with minimum lattice strain. Besides, Te atoms is positively charged because the electronegativity of Te is smaller than that of O. Consequently, Te atom is expected to act as an isoelectronic donor in ZnO. Moreover, the acceptor level of N doped ZnO is narrow and deep. While in the Te-N doped ZnO system, N-impurity bandwidth at the top of valence band becomes larger, while tends to delocalize the hole. Meantime, the system obtains shallower acceptor levels and lighter mass of acceptors. The results suggest that the codoping of Te-N is an effective p-type doping method in ZnO.