The N-doping effects on the electronic and optical properties of TiO2 rutile crystal have been studied using density functional theory (DFT). The calculations of several possible N-doped structures show that band gaps have little reduction but some N 2p states lie within the band gap in the substitutional N to O structure and interstitial N-doped rutile supercell, which results in the reduction of the photon-transition energy and absorption of visible light. In contrast, substitutional N to Ti doped model has a significant band-gap narrowing. The results maybe clarify confusions in nitrogen-doped TiO2 rutile crystal.