In situ low-temperature scanning tunneling microscopy is used to study the growth of 3,4,9,10-perylene tetracarboxylic dianhydride (PTCDA) on epitaxial graphene (EG) on 6H-SiC(0001), as well as on HOPG for comparison. PTCDA adopts a layer-by-layer growth mode, with its molecular plane lying flat on both surfaces. The PTCDA films grow continuously over the EG step edges, but not on HOPG. STS performed on single-layer PTCDA on monolayer EG shows a wide band gap larger than 3.3 eV, consistent with pristine PTCDA films. Synchrotron-based high-resolution photoemission spectroscopy reveals weak charge transfer between PTCDA and EG. This suggests weak electronic coupling between PTCDA and the underlying EG layer.