In order to clarify the edge and interface effect on the adhesion energy between graphene (Gr) and its substrate, a theoretical model is proposed to study the interaction and strain distribution of Gr/Si system in terms of continuum medium mechanics and nanothermodynamics. We find that the interface separation and adhesion energy are determined by the thickness of Gr and substrate. The disturbed interaction and redistributed strain in the Gr/Si system induced by the effect of surface and interface can make the interface adhesion energy decrease with increasing thickness of Gr and diminishing thickness of Si. Moreover, our results show that the smaller area of Gr is more likely to adhere to the substrate since the edge effect improves the active energy and strain energy. Our predictions can be expected to be a guide for designing high performance of Gr-based electronic devices.