By the full-potential linearized augmented plane-wave method (FP-LAPW), we investigate the electronic structure, the band structure, the dielectric function, the absorption spectrum, the reflectivity and the refraction of Cr doped SnO2 superlattice. The generalized gradient approximation (GGA) is used for handling correlation energy. Calculation results show that due to the Cr doping, SnO2 superlattice forms new electron occupied state near Fermi energy level and uncentinuous impurity band comes into being, which is contributed by Cr-3d and O-2p, Sn-5s. In dielectric spectrum appear three new dielectric peaks between 0 eV to 5.5 eV. In high-energy area, the position of main peak has a blue-shift and the peak intensity reduces. Absorption spectrum, reflectivity spectrum and refraction spectrum also have peaks corresponding to the dielectric peaks, which are caused by d—d transition of Cr atom.