We report graphitic carbon growth on crystalline and amorphous oxide substrates by using carbon molecular beam epitaxy. The films are characterized by Raman spectroscopy and X-ray photoelectron spectroscopy. The formations of nanocrystalline graphite are observed on silicon dioxide and glass, while mainly sp2 amorphous carbons are formed on strontium titanate and yttria-stabilized zirconia. Interestingly, flat carbon layers with high degree of graphitization are formed even on amorphous oxides. Our results provide a progress toward direct graphene growth on oxide materials.PACS: 81.05.uf; 81.15.Hi; 78.30.Ly.