Based on the first-principle calculations, we present a study for p-type ZnO doping. The calculated results show that (F, Li) codoping can suppress the formation of interstitial Li because the formation energy of FO-LiZn is lower than that of FO-Lii under O-rich condition. However, it is also found that FO-LiZn codoping could not realize p-type ZnO because FO-LiZn forms a fully passive complex. Interestingly, we further find FO-2LiZn is a stable acceptor that has lower formation energy and shallower transition level under O-rich condition. We expect this study might be helpful for synthesizing good p-type ZnO by controlling (F, Li) codoping.