Abstract: Based on density functional theory (DFT) of the first principles, the electronic structures, total density of states (DOS) and elastic constants of anatase-TiO2 are investigated by Cambridge serial total energy package (CASTEP) program. The orbits of Ti and O are also discussed; it is found that the TiO2 is the semiconductor with the indirect band gap about 2.2 eV. The results indicate that there are obvious electron transition between O and Ti atomic, and electron is visibly localized. The partial covalent bond is existed due to the hybrid orbital. In tetragonal crystal system, TiO2 is characterized with the high bulk modulus about 204.44GPa because of the network structure of complex bonds, the system is lack of gliding planes, materials are easily broken by brittle fracture; and the shear modulus is relatively low only about 64.71GPa.