The crystal structures,band structures,density of states and optical properties of Ti and O vacancies in rutile TiO_2in comparision with those of pure rutile TiO_2are investigated,by using the first-principles based on density functional theory (DFT) method and the norm conserving pseudopotential scheme.The obtained results show that both vacancy-doped struc tures exhibit a weak magnetism,and a larger bond length and atomic population for Ti-O bond.The co nduction band gaps decrease and both conduction and valence bands move towards the low energy direc tion in the vacancy-doped structures,and the contribution of atomic vacancy carriers thus enhances the ele ctrical conductivity of the system.By introducing vacancies in rutile TiO₂,the Ti-vacancy phase s hows a p-type semiconducting nature with energy gap of 1.816eV,and the O-vacancy phase shows an n-type semiconducting nature with energy gap of 1.961eV.Meanwhile,the dielectric pea ks of the vacancy-doped structures display a significant red shift,and possess a higher abs orption coefficient than that of pure TiO_2in the visible region.Compared with O-vacancy structure,the larg er dielectric constant, refractive index and extinction factor for visible light absorption intensity i n Ti-vacancy structure would enhance the optical transitions for low-energy electrons and possess better cat alytic properties of visible light.