Photoluminescence (PL) property data for reported α-Si₃N₄ to date are scattered and it is difficult to clarify the reason only through experimental study. In this paper, the relationship between photoluminescence and intrinsic point defects in α-Si₃N₄ has been established accordingly via band structure modelling based on density functional theory calculation. The results show that band structures of α-Si₃N₄ are significantly affected by the locations of defect levels, which are changed with various partial atomic structures around point defects. Formation energies are also calculated to determine the main types of intrinsic point defects in α-Si₃N₄ under different conditions (Si-rich or N-rich). The results suggest that multiple types of intrinsic point defects coexist in α-Si₃N₄, leading to various electronic transition modes. Furthermore, combined with the calculated results, the discrete photoluminescence data for α-Si₃N₄ are revealed by electronic transition modes under different conditions. The main visible luminescent peaks are attributed to the electron transitions of E_c → Si˙ σ and Si˙ σ → E_v for Si abundant α-Si₃N₄, while N₄⁺ → N₂⁰ for N plentiful α-Si₃N₄.