Luminescence is emission of light by a substance not resulting from heat. It is form of cold body radiation. It can be caused by chemical reactions of the substance with other substances around it, electrical energy, subatomic motions or stress on a crystal. There are many types of luminescence. One of it is phosphorescent. Phosphorescent is made from phosphors such as doped strontium aluminate. Phosphorescent emission light persists long after it has been exposed to light and will fading over time. Promethium (Pm) is low energy beta emitter. It does not degrade the phosphor lattice and the luminosity of the material does not degrade so fast. Promethium based paints are safer than Radium (Ra) and have half-life about more than two years. Promethium usually found in form oxidation called promethium (III) oxide (Pm2O3) and usually applied on watch and phones dial. The study of a band structure of Pm2O3 has not been covered yet. By using density functional theory, we calculated the band gap of promethium (III) oxide from it crystalline structure. The calculated band structure show a clear band gap between valence and conduction band at Fermi level. However the value shows very small gap at 0.286 eV. The density of state and partial density of states has been produced. The calculation has been done using different type of approximation from general gradient approximation (GGA).