The effects on the ferromagnetism of the O or Zn defect in Cu-doped ZnO with the concentration of 2.77-
8.33% have been investigated by the first-principles calculations. The Cu doping in ZnO was calculated to be a kind of p-type ferromagnetic half-metals. When the Zn vacancy exists in Cu-doped ZnO, the Cu magnetic moment increases, while for the O vacancy it is reduced. It is noticeable that the ferromagnetic state was originated from the hybridized O(2p)-Cu(3d)-O(2p) chain formed through the p-d coupling. The carrier-mediated ferromagnetism by nitrogen or fluorine does not depend on their concentration.