Based on first principles within the density-functional theory, using the plane-wave ultrasoft pseudopotential method, the models of unit cell pure ZnO and two highly Ga/N co-doped supercells of Zn0.9375Ga0.0625O0.9375N0.0625 and Zn0.875Ga0.125O0.75N0.25 with different doping concentrations are constructed, and the geometry optimizations for the three models are carried out. The total density of states and the band structures are also calculated. The calculation results show that at a higher doping concentration, when the co-doping concentration is more than a special value, the conductivity decreases with the increase of Ga/N co-doping concentration in ZnO, furthermore the red shift effect is more prominent which is consistent with the change trend of the experimental results.