We present the band structures and densities of states and calculation of absorption spectrum as well as the relative number of electrons and mobility ratio of electrons scattering from Zn1-xGaxO with different concentration of Ga，　and in the condition of high concentration of Ga heavily doped in ZnO semiconductor at low temperature，　by adopting the ab-initio plane wave ultra-soft pseudo potential technique based on the density functional theory. It was found that the relative number of electrons increases with the concenteation of Ga increasing，　but the mobility ratio of electrons of Zn1-xGaxO decreases. The conductivity and minimum band gaps of the doped and undoped ZnO have been compared respectively，from which　we draw the conclusion that the conductivity of Zn1-xGaxO semiconductor decreases with the concentration of Ga increasing. When the concentration of Ga reaches a certain value，　the minimum band gap dreases with the concentration of Ga increasing，　and the phenomenon of red shift happens in the high energy zone. Calculations is in agreement with the experimental results obtained in Zn1-xGaxO with atomic Ga doping in excess of x=004.