We studied the stacking sequence of graphite films formed by the thermal decomposition of a vicinal (titled 4℃ toward the  direction) 6H-Si (0001) substrate surface. Thin (typically three layers) graphite films grown by annealing at 1400℃ or 1500℃ showed clear low-energy election diffraction (LEED) patterns with threefold rotational symmetry. This indicates that one of two equivalent domains of graphite films formed after annealing at 1900℃ exhibited Bernal (AB…) stacking preferentially. On the other hand, a sixfold rotational symmetry was found on the flat (not inclined) sample surface after annealing at 1400℃due to mixed rotational domains and various graphite thicknesses. These results show that better-quality graphite films were achieved on the vicinal surface than on the flat surface.