The local structures and 4f -> 5d transition energies of Ce3+ located on the two crystallographic strontium sites of Sr3AlO4F, with charge compensation by means of nearby sodium substitutions for strontium (Na-sr') or oxygen substitutions for coordinating fluorine (O-F') have been studied using the density functional theory (DFT) within the supercell model and the wave function-based embedded cluster calculations, respectively. The DFT total energy calculations show that Ce3+ prefers strongly to occupy the eight-coordinated (Sr2) site over the ten- coordinate (Srl) site. On the basis of the results from embedded cluster calculations at the CASPT2 level with the spin-orbit effect, the experimentally observed excitation bands are identified in association with the charge-compensated cerium centers. Especially, the two bands observed at similar to 404 and similar to 440 nm have been both assigned to the Ce3+ located at the Sr2 sites but with compensation by one and two nearest-neighbor O-F' substitutions, respectively, rather than to the Ce3+ on the Srl and the Sr2 sites, respectively, as proposed earlier. Furthermore, the structural and electronic reasons for the red shift of the lowest 4f -> 5d transition caused by coordinating O-F' substitutions are analyzed in terms of the variations in centroid energy and crystal-field splitting of the 5d(1) configuration with the local environment. Finally, the thermal quenching of 5d luminescence at relatively high Ce3+ concentrations is discussed on the basis of the electronic properties calculated with the hybrid DFT method.