In this paper, we present the experimental result as well as the theoretical calculation of the electronic band structures and the optical absorption spectra for N-doped and Fe-doped TiO₂ anatase. The main purpose is to provide evidence in the viewpoint of visible light photocatalytic activity of N-doped and weak ferromagnetism of Fe-doped in TiO₂ anatase. Accordingly, to evaluate the separate contributions of nitrogen doping and iron doping in anatase, we present the results of spin-polarized density functional theory (DFT) calculations that have been used to calculate the electronic band structures and optical absorption spectra that arise for a range of concentrations of (i) substitutional nitrogen and (ii) substitutional iron in anatase TiO₂. Our results show that absorption in the visible range is mainly due to nitrogen states located above the valence bands, whereas weak ferromagnetism of Fe-doped in TiO₂ anatase is mainly caused by spin polarization. These results have important implications for the understanding and further development of photocatalytic materials that are active under visible light. These findings agree favorably with our own experimental data and enable conclusions to be drawn about the nature of the practical catalyst in N-doped and the ferromagnetic origin in Fe-doped TiO₂ anatase.