The electronic structures and optical properties of undoped and La doped 6H-SiC were calculated by the first principle calculation method based on density functional theory. Undoped 6H-SiC is an indirect bandgap semiconductor, whose gap width is 2.045 eV and La-Ce doped 6H-SiC is also an indirect bandgap semiconductor, whose gap is reduced to 0.339 eV, and it is the type of p. The Fermi level is contributed by the electronic orbits of Si-3p and C-2p. The Fermi level of La-Ce doped is mainly contributed by the 5d electronic orbit of La and the 4f electronic orbit of Ce, the 2p electronic orbit of C, the 3p electronic orbit of Si. Only one dielectric peak appears at the doped and undoped 6H-SiC. The reason of the dielectric peak is the transition of valence band electrons to conduction band electrons. The maximum of absorption coefficient of un-doped 6H-SiC is the photon energy of 10.31eVand the maximum of absorption coefficient of La-Ce doped 6H-SiC is the photo energy of 5.85eV.