The hexagonal, monoclinic and cubic structures of Lu₂O₃are studied by the plane wave pseudopotential method based on the first-principles density functional theory. The calculated binding energies reveal that the C-type cubic structure of Lu₂O₃is the most stable. The mechanical properties show that the cubic Lu₂O₃exhibits good ductility and elastic anisotropy. Lu₂O₃is thermodynamically stable. The electronic calculations show the cubic Lu₂O₃ has a direct bandgap. The electrons situated in the bottom of the valance band have the small effective mass and the high degree of nonlocalization. And the electrons transitions between the top of the conduction band and the bottom of the valance band primarily derive from Lu-4f and O-2p states. It forms the covalent bonding of Lu–O by the strong orbital hybridization of 5d orbital of Lu atom and 2p orbital of O atom. The maximal optical reflectivity of the cubic Lu₂O₃ is 0.36 and the optical absorption ability of the cubic Lu₂O₃ is strong in the energy from 3 to 10 eV. Lu₂O₃isa fine optical insulator which has the novel optical properties owning to its perfect transparency in the visibleSandSnearSinfraredSwavelength regions.