The effect of oxygen vacancy in anatase TiO2 crystal on the optical property was studied by using the plane waves ultrasoft pseudopotential technique, which was based on density functional theory. The crystal structure of anatase with oxygen vacancies was optimized by using the first principle. Then electronic-state density , complex refractive index,dielectric functions and absorption spectra in pure and oxygen doped anatase TiO2 crystal were calculated. By comparing the results, we find there are some changes in electronic structure, which lead to a change of the interaction between electrons. The Fermi surface of the total density of states (TDOS) extends into the conducting band, and causes Mott phase transformation, and the Ti 3d state of the anatase crystal of TiO2 at -6.097 eV shows new split peaks. Positions of imaginary part of dielectric functions and real part of the absorption spectrum and complex refractive index are identified, showing there are inner relations between them, which are related to the state density of the electrons. By theoretical analysis and calculation, we find that the imaginary part of dielectric functions and the peak position of absorption spectrum are caused by the relaxation effect, meanwhile the height of the peaks is related to the transition probability of the electrons, and anisotropism of the crystal is determined by its symmetry structure of crystal.