Using the first-principles plane-wave ultra-soft pseudo-potential method based on the density functional theory, the structures, electronic-structures and optical properties of pure anatase TiO2, N (Cu) doped TiO2, and N/Cu co-doped TiO2 crystal are studied by the local-spin density approximation plus Hubbard U method. It is shown that the lattice constants become larger because of the lattice distortion caused by doping. Impurity levels in the band gap of TiO2 are introduced by N and Cu doping, and the forbidden band width is correspondingly changed. For N doped TiO2, the reduction of the band gap is weak, while the N/Cu co-doped TiO2 band gap decreases remarkably. It leads to a red shift of visible absorption spectrum and enhances optical catalysis. The effect is useful for the practical application of photo-catalytic.