Curcumin loading capacity of polyethylene glycol (PEG) functionalized graphene and graphene oxides are investigated using molecular dynamics and Monte Carlo (MC) adsorption locator simulations. These simulation methods were performed as a function of oxidation extent to study the effect of functional groups on curcumin loading and release properties. Adsorption locator energy calculations suggest that the curcumin drug molecule prefers to adsorb at the less oxidized sites of graphene oxide. One of the phenolic rings of curcumin drug prefers to have a planar interaction with graphene and graphene oxide framework due to the pi-pi interaction. Molecular dynamic studies are conducted in aqueous medium under neutral pH. Mean square displacement and radial distribution functions are obtained to determine the nature of the curcumin attachment and release in aqueous medium. The molecular simulations show that separation distance of the curcumin molecule from GO sheet is 4.4 Å. The molecular simulations presented in this work will help to design new synthetic methods of nanocarriers for curcumin delivery applications.