Monolayer and bilayer graphene films with a few hundred nm domain size were grown on ultraprecision figured 4H-SiC(0001) on-axis and 8 degrees -off surfaces by annealing in ultra-high vacuum. Using X-ray photoelectron spectroscopy (XPS), atomic force microscopy, reflection high-energy electron diffraction, low-energy electron diffraction (LEED), Raman spectroscopy, and scanning tunneling microscopy, we investigated the structure, number of graphene layers, and chemical bonding of the graphene surfaces. Moreover, the magnetic property of the monolayer graphene was studied using in-situ surface magneto-optic Kerr effect at 40 K. LEED spots intensity distribution and XPS spectra for monolayer and bilayer graphene films could become an obvious and accurate fingerprint for the determination of graphene film thickness on SiC surface.