We have performed a study on La heavily doped ZnO, based on the first principles. The calculated results show that with the increase of concentration of La, the lattice parameter is expanded. It is found that the top of valence band maximum is determined by the O-p states and the conduction band minimum is depended on the La-f and La-d states. The band gap of doping system is broadened as the increase of concentration of La, because the valence band moves towards lower energy more than the conduction band does. Furthermore, it is found that heavily doping of La with low concentration can enhance the conductivity of ZnO. The results are helpful to gain a systematic understanding of electrical properties of La-doped ZnO.