Graphene functionalized with dianthracene malonate was synthesized and used subsequently for construction of covalently bound graphene-fullerene hybrid nanomaterials. For this purpose, novel approach of Diels–Alder reaction of C60/C70 fullerene cores with anthracene moieties previously introduced onto graphene surface was successfully employed. Structure and composition of obtained graphene and its derivatives were characterized using scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS) and FT-IR spectroscopy. Obtained results revealed that both C60 and C70 fullerenes were found to be capable of formation desired Diels–Alder adducts, yielding products of different morphology. Capacitive properties of the synthesized energy storage nanomaterials were determined by means of cyclic voltammetry (CV) and galvanostatic charge/discharge (GCD) measurements, revealing that functionalization of graphene with C60 moieties enhances its energy storage properties.