Polyethylene glycol (PEG)-based composite phase change materials (PCMs) are widely employed as energy storage materials in the industries of energy, microelectronics and aerospace due to their excellent thermal and mechanical properties. From the view point of molecular, the effects of graphene functionalization on the thermal and mechanical properties of composites PCMs during phase transition are studied in this paper. It is shown by the results obtained from simulations that the functionalization of graphene surface can decrease the thermal resistance at the PEG-graphene interfaces considerably, and increase the phase change temperature and isobaric heat capacity as well. In terms of mechanical properties, it was found that the Young's modulus and shear modulus of composite PCMs decreased after functionalization, and the not obvious difference was available between the effects of different functionalization on mechanical properties. The present findings provide a better understanding of the thermomechanical mechanism of graphene/PEG composite PCMs and effective guidance for improving their thermophysical properties.