We synthesized Graphene/PNIPAm nanocomposite hydrogels. We demonstrated that the elasticity of the nanocomposite hydrogel is mainly ascribed to the relative area change of the sample around room temperature. Above a lower critical solution temperature, the hydrogel become a compressible at large deformation which leads to the change of water composition. The change of the entropy of mixing between PNIPAm and water by adding graphene is expected to be negligible. But the addition of graphene may affect the enthalpy of mixing in the composite hydrogel. Therefore, we can model the osmotic pressure change by compression by modifying the Flory theory. From the measured first normal stress difference, we evaluated the osmotic pressure change by the compression. At small deformation, the elasticity of the hydrogel follows Neo-Hookean model. At large deformation, the elacticity of the hydrogel follows Mooney-Rivlin model in incompressible regime