Graphene is a fundamentally new type of 2D electronic material exhibits extraordinary properties. In this work, we used the thermal decomposition of SiC in vacuum principle to grow epitaxial graphene on Both C-face and Si-face SiC, that because epitaxial graphene is a reliable candidate for all kind of applications in 2D electronics and it has similar properties to carbon nanotube and graphene grown by exfoliation method, but it is more appropriate for the design of electronic device as it can be grown on wafer-sized scale. We review the physical and electronic properties of graphene and what’s makes it different when compare to the ordinary semiconductors. Since the interest in graphene increases as a perfect candidate for future electronics applications, many methods are used to synthesis graphene. We give a brief review to several methods used to produce graphene. For electronic device applications, graphene should be grown in a high homogeneity, uniformity and with low growth rate. Therefore the growth rate graphene should be controlled to get high homogeneity and uniformity. Raman spectroscopy considers a quick way to detect the presence of graphene, determine the number of the layers and to check the defects in the grown layer. At the wavelength of 514 nm , Raman spectroscopy is used to investigate epitaxial graphene grown on both C-face and Si-face SiC with different parameters and to study the evolution and the proportionality of the grown layers with the time . Finally we used AFM to study the morphology of epitaxial graphene grown on SiC substrate. The morphology of graphene on C-face of SiC is compared with the one on Si-face of SiC.