Graphene as a 2-dimentional material has been widely used in the field of biomedical applications. In this study, molecular dynamics simulations are carried out on the fibrinopeptide-A and graphene surfaces with N and O modifications. A new set of parameters for the CHARMM force field are developed to describe the behaviors of the surfaces. Our results indicate that the existence of most oxygen and nitrogen groups may enhance the interaction between the surfaces and the peptide, whereas the substitutional nitrogen on the graphene surface does not make a big difference. The improvement of interaction is not only because of the functional group on the surface, but also the defective morphology. The defective morphology also clears away the surface water layer. Our results suggest that the interactions between graphene biomolecules can be affected by functionalizing the surface with different types of functional groups, which is in accordance with the theory of material design.