This paper demonstrates that a highly thermal stable and tunable-luminescence phosphors Y₃Al₂Ga₃O₁₂: Tb³⁺, Eu³⁺ with efficient energy transfer, which is prepared by the high-temperature solid-state reaction. First-principles method is performed to analyze the electronic structures, band structure, density of states and formation energy of Y₃Al₂Ga₃O₁₂: Tb³⁺, Eu³⁺. For high luminescence output, Y_3-xAl₂Ga₃O₁₂: xTb³⁺ and Y_3-yAl₂Ga₃O₁₂: yEu³⁺ with high concentration quenching (x = 0.5 and y = 0.7) are achieved. The effect of energy transfer from Tb³⁺ to Eu³⁺on emission color tuning and luminescence thermal stability is studied. The energy transfer efficiency from Tb³⁺ to Eu³⁺ reaches as high as 74.2% and emission color can be tuned from green, yellow and red by adjusting the ratio of Tb³⁺/Eu³⁺. What's more, Y₃Al₂Ga₃O₁₂: Tb³⁺, Eu³⁺ phosphor exhibits a good thermal stability, of which emission intensity still keeps 60% at 150 °C.