Graphene, one-atom-thick planar sheet of carbon atoms densely packed in a honeycomb crystal lattice, has grabbed appreciable attention due to its exceptional electronic, mechanical and optical properties. Chemical functionalization schemes are needed to integrate graphene with the different materials required for potential applications. Molecular self-assembly behavior on graphene is a key method to investigate the mechanism of interaction between molecules and graphene and the promising applications related to molecular devices. In this thesis, we report the molecular self-assembly behavior of phenyl-C61-butyric acid methyl ester (PCBM), C60, perylenetetracarboxylic dianhydride (PTCDA) and Gd3N@C80 on flat and rippled graphene 2D material by the experimental methods of scanning tunneling microscope (STM) and atomic force microscope (AFM) and by the theoretical method of density functional theory (DFT). We found that molecules form ordered structures on flat graphene, while they form disordered structure on rippled graphene. For example, PCBM forms bilayer and monolayer structures, C60 and Gd3N@C80 form hexagonal close packed (hcp) structure on flat graphene and PTCDA forms herringbone structure on flat graphene surface. Although C60 and Gd3N@C80 both form hcp structure, C60 forms a highly ordered hcp structure over large areas with little defects and Gd3N@C80 forms hcp structure only over small areas with many defects. These differences of structure that forms on flat graphene is mainly due to the molecule-molecule interactions and the shape of the molecules. We find that the spherical C60 molecules form a quasi-hexagonal close packed (hcp) structure, while the planar PTCDA molecules form a disordered herringbone structure. From DFT calculations, we found that molecules are more effected by the morphology of rippled graphene than the molecule-molecule interaction, while the molecule-molecule interaction plays a main role during the formation process on flat graphene. The results of this study clearly illustrate significant differences in C60 and PTCDA molecular packing on rippled graphene surfaces.