The formation energies and ionization energies of Ag-N dual-doped ZnO and interstitial N and H monodoped ZnO:(Ag,N) are investigated from the firstprinciples pseudo-potential approach based on density functional theory. It is found that AgZn-NO accepter pair has lower formation energy and ionization energy than Ag-N related to acceptor clusters, which demonstrates that the p-type conductivity of Ag-N dual-doped ZnO system is mainly attributed to the formation of the accepter pairs. Moreover, when ZnO:(Ag,N) system has additional N atoms in some interstitial sites of ZnO crystal, interstitial N atom and AgZn-NO accepter pair prefer to bind together to form AgZn-(N2)O donor complex which lowers doping efficiency, which is not conducive to p-type conductivity. For H doping in the ZnO:(Ag,N) system, the interstitial H atoms also prefer to bind to the AgZn-NO accepter pair, forming acceptor-donor-acceptor (AgZn-H#em/em#-NO) triplet, which not only enhances the incorporation of acceptors (AgZn-NO) but also gives rise to a shallower acceptor level in the band gap in p-type ZnO crystal. Thus, it is suggested that H-assisted Ag-N codoping is an effective method of p-type doping in ZnO.