This work presents a procedure for functionalization of graphene sheets from edges by polyglycerol. Hyperbranched polyglycerol with a bi-dentate aromatic segment in its focal point was synthesized and used to sandwich graphene sheets from the cut-edges. Due to the hydrophobicity of the flat surface of the edge-functionalized graphenes and hydrophilicity of their edges, they changed their conformation from the extended- to the closed-state and formed nanocapsules in aqueous solutions. Spectroscopy and microscopy evaluations showed that the average size for nanocapsules is 300 nm. They were able to encapsulate hydrophobic molecules such as doxorubicin in aqueous solutions with a high loading capacity. Aqueous solutions of nanocapsules and those with encapsulated doxorubicin were stable at room temperature for several weeks. Due to their unique properties including suitable size and shape, stability in aqueous solutions, and high loading capacity for hydrophobic anticancer drugs, graphene-based nanocapsules are promising systems in order to use in nanomedicine, especially for future cancer therapy.