In this paper, we represent a theoretical study of the (Zn, Mn)O doped system with native point defects of ZnO as oxygen interstitials (O-i) and zinc vacancies (V-Zn). Under these defects, it has been shown that the ground state can be converted from spin glass to ferromagnetic phase, by performing ab initio density functional theory calculations relying on the Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) method employing the local density approximation (LDA) with the parameterization by Morruzi, Janak, and Williams. The stability of magnetism in the (Zn, Mn)O doped system with different native point defects has been discussed. We find that acceptor-like defects (that is, O-i, O-Zn, and V-Zn) may cause the enhancement of the ferromagnetic characteristics in ZnMnO with increasing T (c) . Based on the theoretical results, we suggest that the native point defects have a key role with respects to the FM properties. Using the mean field approximation, the Curie temperature in our studied model is estimated.