The electronic structure and luminescence of BaF₂ crystal are investigated using both self-consistent one-electron nonrelativistic Hartree-Fock-Slater and relativistic Dirac-Slater discrete variational-local density functional methods with an embedded cluster model. The energy levels, densities of states and spin-orbit coupling energy were obtained in good agreement with the experimental results. We verified that the fast luminescence components are the transitions of electrons from the F^-(2p) valence band to the cation Ba²⁺(5p_3/2) level, and pointed out that the necessary condition that the energy difference between the valence band and the core band must be smaller than the energy gap, for observing the fast luminescence components, is satisfied.