We report microscopic Raman scattering studies of epitaxial graphene grown on SiC substrates using a deep-ultraviolet (UV) laser excitation at 266 nm to elucidate the interaction between the graphene layer and the substrate. The samples were grown on the Si-face of vicinal 6H-SiC (0001) substrates by sublimation of Si from SiC. The G band of the epitaxial graphene layer was clearly observed without any data manipulation. Increasing the number of graphene layers, the peak frequency of the G-band decreases linearly, while the peak width and the intensity increase. The G-band frequency of the graphene layers on SiC is higher than those of exfoliated graphene, which has been ascribed to compression from the substrate.