The electronic structures of potassium doped ZnO have been calculated by first principles plane wave-function psuedopotential approach based on density-functional theory and local density approximation. Properties of some defects were studied in order to explicate the conductivity mechanism of p-K:ZnO, including hydrogen interstitial (Hi), oxygen vacancy (VO), zinc interstitial (Zni) and zinc vacancy (VZn). The calculated results revealed that: (1) K-doping introduced a shallow acceptor,besides increasing the system total energy simultaneously. (2) K-H:ZnO decreased the system energy and increased the system stability. (3) Although the formation of VO was more difficult than that of Zni, both of them were electronegative centers and played a role in compensating for the acceptors. (4) VZn produceda shallow acceptor approximately 0.5 eV above the maximum valence band, which was beneficial for p-type conductivity. Finally, it was proposed that the realization of p-type conductivity in K:ZnO may be due to the formation of a KZn-O-Hi-O-VZn complex.