Band structures,density of states and optical properties of pure,N-doped,S-doped and N-S co-doped rutile TiO₂ are studied with plane-wave ultrasoft pseudopotential method based on first-principles density functional theory.It shows that the gap of N-doped TiO₂ reduces to 1.43 eV,and there is an impurity band on top of the valence band.S-doped TiO₂ results in Fermi level moves to the conduction band,and the gap decreases to 0.32 eV.N-S co-doped TiO₂ results in two impurity bands located in the band gap.One impurity band is apart from the bottom of conduction band by 0.35 eV,the other is apart from the top of valence band by 0.85 eV,which is mainly formed by N-atom 2p orbital and S-atom 3p orbital.It causes a red-shift in absorption wavelength,and gives rise to extremely great absorption coefficient in visible-light region,which shows a strong photocatalytic activity.