Currently, the stability and visible light properties of Ga-2N co-doped ZnO systems have been studied extensively by experimental analysis and theoretical calculations. However, previous theoretical calculations arbitrarily assigned Ga- and 2N-doped sites in ZnO. In addition, the most stable and possible doping orientations of doped systems have not been fully and systematically considered. Therefore, in this paper, the electron structure and absorption spectra of the unit cells of doped and pure systems were calculated by first-principles plane-wave ultrasoft pseudopotential with the GGA+U method. Calculations were performed for pure ZnO, Ga-2N supercells heavily co-doped with Zn1−xGaxO1−yNy (x=0.03125−0.0625, y=0.0625−0.125) under different co-doping orientations and conditions, and the Zn16GaN2O14 interstitial model. The results indicated that under different orientations and constant Ga-2N co-doping concentrations, the systems co-doped with Ga-N atoms vertically oriented to the c-axis and with another N atom located in the nearest-neighboring site exhibited higher stability over the others, thus lowering formation energy and facilitating doping. Moreover, Ga-interstitial- and 2N-co-doped ZnO systems easily formed chemical compounds. Increasing co-doping concentration while the co-doping method remained constant decreased doped system volume and lowered formation energies. Meantime, co-doped systems were more stable and doping was facilitated. The bandgap was also narrower and red shifting of the absorption spectrum was more significant. These results agreed with previously reported experimental results. In addition, the absorption spectra of Ga-interstitial- and 2N-co-doped ZnO both blue shifted in the UV region compared with that of the pure ZnO system.