Under the same condition，ZnO models with different sizes are proposed by using the plane wave ultra-soft pseudopotential technique based on the density functional theory （DFT）. Al and N with different concentrations are heavily doped in ZnO semiconductor，and the density of states of Al and N doped ZnO is calculated by DFT mothod under the condition of low temperature. The relative average number of holes and the scattering mobility of holes in the valence band are calculated. We find that heavily doping of Al-2N atoms with low concentration can enhance the conducting of ZnO，which means that the conductivity of ZnO semiconductor is related with not only the concentration of heavy doped Al and N，but also the relative average number of holes and the scattering mobility of holes in the valence band. The calculated results agree with the experimental results.