Based on the density functional theory (DFT), and using the first-principles plane-wave ultrasoft pseudopotential method, we set up models for a pure ZnO and four different concentrations of Ga-doped ZnO, and the geomertry optimization for the four modes was carried out. The total density of states (TDOS), the band structures (BS) and absorption spectrum were also calculated. Results show that the range of Ga doping amount is limited to 2.08 at% to 6.25 at% in this paper; when the doping concentration of Ga increases, the volume change of the system is not obvious; however, when is energy increases, the system will be unstable, the Burstein-Moss effect of its optical band gap will increase, and the absorption spectrum will shift to high energy. The results of calculation agree with the experimental data.