A series of nitrogen-doped zinc oxide (ZnO:N) thin films were grown on c-plane sapphire substrate by plasma-assisted molecular beam epitaxy. Due to the large number of donor defects, the samples grown in the continuous zinc-rich atmosphere showed n-type conductivity. In order to suppress the compensation effect caused by donor defects, by periodically supplying oxygen during the growth and then alternating the growth atmosphere in the growth process, the conflict between nitrogen doping level and intrinsic defects was relaxed partly. Compared to the case without supplying oxygen, the crystal quality of the thin films was improved. And the photoluminescence measurements showed that the oxygen vacancy and the zinc interstitial defects in the thin films were suppressed significantly. The samples showed a high repeatability of p-type conductivity. The carrier concentration of the samples grown by alternating the growth atmosphere can reach 10 cm. This may be an effective method to realize the p-type doped ZnO.