The formation of B defect, the crystal structure, formation energies, density of states and electronic structure of B-N codoped ZnO were studied using first-principles pseudo-potential approach of the plane wave based upon the density functional theory（DFT）.The study reveals that most of the B atom will present in as-doped ZnO in the form of BZn, which could result in the shrinkage of ZnO unitcell.Compared with N doped ZnO, B-N codoped ZnO has a lower formation energy, correspondingly a higher chemical stability, so its formation is more realizable. Moreover, the acceptor levels of B-N doped ZnO are shallower, resulting in a decreased ionization energy as well as a higher acceptor density.The bonding power of Zn-N is increased in as-doped ZnO, the properties of acceptors are also improved, therefore B-N codoping is expected to be a more efficient way to fabricate p-type ZnO.