A stable and repeatable p-type ZnO is the key to realize the practical applications of photoelectric devices. Nitrogen has been considered as a possible acceptor dopant for p-type ZnO for a long time. However, the low solubility of nitrogen acceptor at oxygen site in ZnO is considered to be one of the main obstacles for p-type ZnO. In this paper, B/N co-doped p-type ZnO thin films were grown on sapphire substrate by plasma-assisted molecular beam epitaxy. The effect of boron on the nitrogen doping was studied by comparing with the single nitrogen doped thin films. X-ray photoelectron spectroscopy demonstrated there exists boron and B-N bond in the ZnO thin film. Compared to the single N-doped sample, B/N codoped samples present much higher carrier density. And the ZnO:(B, N) thin films show stable p-type conduction in two years. It is attributed to the increase of solubility of nitrogen acceptor. It benefits from the strong B-N bonding and weak donor character of boron at zinc site. Boron will not bring strong compensation for acceptors. It suggests that boron is a good co-doping candidate for nitrogen doped ZnO thin films.