We report that graphene films with thickness ranging from 1 to 7 layers can be controllably synthesized on the surface of polycrystalline copper by a chemical vapour deposition method. The number of layers of graphene is controlled precisely by regulating the flow ratio of CH4 and H2, the reaction pressure, the temperature and the reaction time. The synthesized graphene films were characterized by scanning electron microscopy, transmission electron microscopy, selected area electron diffraction, X-ray diffraction and Raman spectroscopy. In addition, the graphene films transferred from copper to other substrates are found to have a good optical transmittance that makes them suitable for transparent conductive materials.