Based on density functional theory of first principles, the states ( DOS) , band structure and multi-optical properties of various supercells structure of S1-xNxO2 have been studied by generalized-gradient approximation (GGA) using WIEN2K. The results show that Fermi levels of all N-doped SnO2 systems shift to lower energy, the band gap get more and more narrow as the doping concentration increasing, and formed a localized state in the energy range of 1. 35-2. 50 eV, the main source is N 1p. By analyzing band structure of Sn1-xNxO2, N-doped SnO2 systems were direct transition semiconductor. The imaginary part of the dielectric function and refractive makes a red shift corresponding to the band gaps, the transition peaks of the dielectric function related to the transition and absorption of electrons between the valence band and conduction band, and pointed out the intrinsic relationship between optical properties and electronic structure in theory.