The (100-x)Ga2O3-xZnO-0.1MnO and 51Ga2O3-49ZnO1MmOn-0.1MnO powders (MmOn: additives, Li2O, Na2O, K2O, MgO, CaO, ZnO, SrO, BaO, B2O3, Al2O3, Ga2O3, Y2O3, La2O3, In2O3, SiO2, TiO2, GeO2, P2O5, Nb2O5, Ta2O5, MoO3, and WO3) were prepared by a solid-state reaction at 1000 degrees C for 5 h in the air. In (100-x)Ga2O3-xZnO-0.1MnO powders, a green luminescence band due to the 4T1(4G)-> 6A1(6S) transition of Mn2+ ions appeared at 505 nm under excitation at 245 nm. It has the maximum intensity in the chemical composition (x = 48.5) with the largest number of distorted and octahedrally coordinated Ga3+ ions with an oxygen vacancy (distorted GaO57- groups). It was found that the Mn2+ green luminescence occurred mainly because of the excitation of the distorted GaO57- groups and the energy transfer from distorted GaO57- groups to Mn2+ ions. In 51Ga2O3-49ZnO-1MmOn-0.1MnO powders, the lower the basicity of MmOn, the stronger was the integrated intensity of the Mn2+ green luminescence. It was revealed that the MmOn with lower basicity had the ability to form the distorted GaO57- groups. The integrated intensity of the Mn2+ green luminescence was most enhanced by the addition of B2O3 with low basicity.