Recently, improving the visible-light utilization ratio by the metal and non-metallic impurities co-doped TiO2 semiconductor is a research focus. The band structure, density of states, partial density of states and optical properties of Mn-doped, N-doped and Mn-N co-doped anatase TiO2 are studied by plane-wave supersoft pseudopotential method based on the density functional theory. Contrasting Mn, N, Mn-N doped anatase TiO2, the results show that N single doped TiO2 effectively makes the band gap decrease from 3.2 eV to 2.83 eV and a Mn single doping results in three impurity levels in the band gap, which reduces the electron transition energy from the valence band to conduction band. While Mn-N co-doped anatase TiO2 crystals lead the Fermi level to move to the conduction band, simultaneously forming impurity level in the valence band top and reducing the band gap. The electronic transition energy is about 2.1 eV (wavelength is 590 nm) from impurity levels to the conduction band, which exactly corresponds to the absorption peak in the absorption spectrum. This will more effectively improve the utilization of the visible light.