The crystal structure, the band structure, and the density of states of anatase TiO2 are analysed by using the plane-wave ultrasoft pseudopotential method of the first principles based on the density functional theory. Then we calculate optical properties such as dielectric function, energy loss function, photoconductivity systematically based on the results of electronic structure, and analyse the correlation of electronic structure with birefringence and anisotropy. The obtained results are consistent well with the reported results in the literature, revealing the natures of electronic structure of TiO2 and its birefringence as well as anisotropy theoretically.