Rutile-monoclinic phase transitions of vanadium oxide (VO2) nanocrystals adsorbed on graphene-based substrates are of current scientific interest, although their adsorption and growth mechanisms have not been investigated theoretically. In this study, we use density functional theory (DFT) calculations for determining the binding energies and predicting the corresponding directions of growth of VO2 nanostructures (rutile and M1-monoclinic) interacting with both pure graphene and functionalized graphene nanoribbons. Several adsorption sites of pure graphene including the top, bridge, and hollow sites are considered, while additional adsorption sites of functionalized graphene nanoribbons, epoxy, alcohol and carboxylate are investigated. Vanadium oxide nanostructures are found to favor physical adsorption on the hollow sites of pure graphene, while chemical adsorption is favored on the carboxylate sites of functionalized graphene nanoribbons (FGNRs). Charge density maps showed the electron distribution originating from the interaction between VO2 and graphene substrates, helping to understand the mechanism of charge transfer. Electronic local potentials showed vertical growth tendencies for rutile VO2, while M1-monoclinic VO2 showed horizontal growth tendencies. Partial density of states (PDOS) helped examine the electronic structure of metallic rutile VO2 binding to hollow and carboxylate sites of functionalized graphene. These results provide an improved understanding of the controlled and oriented growth of VO2 nanocrystals on graphene-based substrates which can enable various properties such as the metal-insulator transition (MIT) of VO2 in light regulation applications.