Ag-N dual-doped ZnO films have been fabricated by a chemical bath deposition method. The p-type conductivity of the dual-doped ZnO:(Ag, N) is stable over a long period of time, and the hole concentration in the ZnO:(Ag, N) is much higher than that in mono-doped ZnO:Ag or ZnO:N. We found that this is because AgZn-NO complex acceptors can be formed in ZnO:(Ag, N). First-principles calculations show that the complex acceptors generate a fully occupied band above the valance band maximum, so the acceptor levels become shallower and the hole concentration is increased. Furthermore, the binding energy of the Ag-N complex in ZnO is negative, so ZnO:(Ag, N) can be stable. These results indicate that the Ag-N dual-doping may be expected to be a potential route to achieving high-quality p-type ZnO for use in a variety of devices.