The nonvalent interaction between amphiphilic polymers and graphenes is important to provide the surface functionalization of graphene. Herein, molecular dynamics simulations were carried out to investigate the interaction of pyrene-polyethylene glycol (Py-PEG) with graphene. The dynamic adsorption process and self-assembly morphology of Py-PEG onto nanoscale graphene surface have been demonstrated. The effects of the graphene size and the length of polymer chain were explored. It was shown that Py-PEG could spontaneously adsorb onto graphene surface. The Py-PEG polymer generally exhibits a coil structure with the hydrophobic pyrene surrounded by the PEG chain. However, once the Py-PEG molecule approaches the graphene surface, the PEG chain can unfold its structure on the graphene surface and the pyrene group can display a flat binding mode with the surface. Comparatively, the water solvent has an obvious impeding effect on the surface adsorption due to the hydrogen bonding interaction between PEG chain and water molecules. The thermodynamic free energy shows that the interaction between pyrene and carbon surface provides the main interaction contribution to the adsorption performance. (C) 2013 Elsevier Inc. All rights reserved.