With the molecular beam epitaxy technique, layer-by-layer growth of atomically flat topological insulator Bi2Te3 and Bi2Se3 thin films has been realized on Si(111) and graphene substrates, respectively. The growth criteria by which intrinsic topological insulators can readily be obtained is established. By using in situ angle-resolved photoemission spectroscopy and scanning tunneling microscopy measurements, the band structure and surface morphology of Bi2Te3 and Bi2Se3 thin films of different thickness can be studied. Molecular beam epitaxy technique was shown to not only provide an excellent method to prepare high quality topological insulators but show possibilities of engineering their electronic and spin structures as well, which is of significant importance for potential applications of topological insulators based on well-developed Si technology.