Using first-principles full potential linearized augmented plane wave method (FP-LAPW), we present the isosurface of spin density, total density of states and optical properties of undoped SnO2, substitutional N for O and substitutional N for Sn in SnO2. The results show that the band gap in two kinds of N-doped SnO2 is wider than that of SnO2 eigenstate, and the imaginary part of the dielectric function makes a blue shift corresponding to the increasing band gaps. It points out the relationship between electronic structure and optical properties in theory.