We have calculated the optical properties of anatase TiO2 and anatase TiO2 by N-doping by plane-wave pseudo-potential method (PWP), namely the imaginary part of dielectric function ε2(ω),the optical absorption coefficient I(ω) and the reflectivity R(ω). We have given an explanation in terms of band structures why the optical spectrum has three main peaks around 2.93 eV,3.56 eV and 3.97 eV after N-doping. Our studies of the optical spectra show that the Red-shift will happen after N-doping, and experimental phenomena also approve the result.