The Raman scattering spectra of the nitrogen doped n-SiC is studied. The theoretical line shape analysis indicates that, compared with 4H-SiC, the shift of the LO phonon-plasma coupled mode in 6H-SiC with free carrier concentration is smaller. From the electronic Raman spectra, which were obtained with laser excitation at 5145nm, there are four spectral lines in 6H-SiC and two lines in 4H-SiC, which correspond to the 1s(A1) to 1s(E) valley orbit transitions at the inequivalent k site. The explanation of the high-frequency signals of 6303 and 635 cm-1 is that they are velated with transitions at active deep level of defect. Finally, the second-order Raman features of 6H- and 4H-SiC are identified using the selection rules for second-order scattering in wurtzite structure.