In this study, nano drug delivery system based on graphene oxide and reduced graphene oxide- polyglycerol hybrids were constructed. Functionalization of nano graphene oxide and reduced graphene oxide was accomplished through noncovalent interaction between the π conjugated system of graphene materials and the aromatic segment in the focal point of polyglycerol polymer. Polyglycerol is a hydrophilic and biocompatible polymer that its conjugation with graphene materials was increased the colloidal stability and decreased the nonspecific interaction of graphene materials. Curcumin as an anticancer hydrophobic natural drug with low systemic bioavailability was simply loaded on these nanohybrids via π-π stacking force between the π conjugated systems of graphene materials and curcumin. Result showed that loading capacity of curcumin for reduced graphene oxide hybrid (49%) is higher than graphene oxide hybrid due to restored of π conjugated system in reduced graphene oxide. Anticancer efficiency of these drug hybrids was investigated by MTT assay. Results showed that these drug carriers have sufficient biocompatibility. Also these nano drug delivery systems showed a cytotoxic effect that was comparable to that of free curcumin. The reduced graphene oxide hybrid is preferred for delivery of curcumin due to its higher loading capacity that can provide efficient dose of drug in low level of carrier