The electronic structures of F-doped SnO2 are calculated by first principles based on density function theory. The cell structures of F-doped SnO2 are optimized and the result shows that the cell parameters remain unchanged after doping. It is found that there are two nonequivalent oxygen sites in the unit cell where one of corresponding oxygen atom will be preferentially replaced by F atoms. Then, the band structures, density of states, partial density of states of undoped and doped SnO2 are calculated using plane wave ultra-soft pseudo-potential method. The influence of F-doping on the electronic structure and properties of SnO2 crystal and the optical absorbtion edge are analyzed. Moreover, the effect of different doping concentration on the electronic structure has been further analyzed.