[en] Based on first-principles theoretical calculations, we investigate the electronic structure of various defects in P-doped ZnO. We find that a PO impurity occupying an O site is a deep acceptor while a PZn atom at a Zn site is the dominant donor, causing a compensation of acceptors. Under O-rich growth conditions, Zn vacancies (VZn) are the main source of p-type conduction. Since VZn is mobile and strongly interacts with abundant PO and PZn defects, resulting complexes, such as PZn-2VZn and PO-VZn, which behave as acceptors, are likely to be formed under non-equilibrium growth conditions, and are responsible for the p-type conduction. We also investigate the effect of the strong Coulomb repulsion for the Zn d electrons on the electronic properties of various defects.