We have investigated the electronic structures of p- or n-type-doped ZnO based on ab initio electronic band structure calculations. We find unipolarity in ZnO; p-type doping using Li or N increases the Madelung energy while n-type doping using Al, Ga, In or F species decreases the Madelung energy. We find a very weak repulsive interaction between Li accepters in Li-doped ZnO (ZnO:Li) with a remarkable increase in the Madelung energy, in contrast with the case of ZnO:N. For ZnO:(2Li, F), total energy calculations show that the formation of the complex with Li-Zn-F-O-Li-Zn which occupy the nearest-neighbor sites is energetically favorable with a decrease in the Madelung energy, which produces low-resistivity p-type ZnO crystals.