A novel growth method (carbon molecular beam epitaxy (CMBE)) has been developed to produce high-quality and large-area epitaxial graphene. This method demonstrates significantly improved controllability of the graphene growth. CMBE with C(60) produces AB stacked graphene, while growth with the graphite filament results in non-Bernal stacked graphene layers with a Dirac-like electronic structure, which is similar to graphene grown by thermal decomposition on SiC (000-1).