We have performed first-principle calculations of electronic band structure of C-doped anatase TiO2, and explained some experimental phenormena of C-doped TiO2s absorption spectrum. The results indicated that the band gap broaders and some new bands appears in the band gap. These new bands result from C 2p orbitals, they are separated, and their existance explains the visible light response. The electrons in the valence band can be excited to the new states and subsequently excited to the conduction band, leading to existence of two absorption edges. Theoretical result are in agreement with the experimental result.