Abstract: The FP-LAPW method was used to investigate the ground-state configurations of Mn-N impurities co-doped p-type ZnO.Based on total energy considerations,we find the case 4（with N and Mn in the proximate layer） was the most stable structure,in the absent of additional hole donors.Our calculations indicate that the Fermi level is positioned near the top of the valence band.And the co-doped system showed half metallic magnetism character.BMP theory was also used to explain the ferromagnetism in the co-doped system.