A preferred embodiment of the present invention is a meso-porous nanocomposite material comprising: (A) nano-scaled graphene platelets, wherein each of the platelets comprises a sheet of graphite plane or multiple sheets of graphite plane, and the platelets have a thickness no greater than 100 nm (preferably smaller than 10 nm) and an average length, width, or diameter no greater than 10 .mu.m (preferably smaller than 500 nm); and (B) an electrically conducting binder or matrix material attached or bonded to the platelets to form the nanocomposite material having liquid accessible pores, which provide a surface area greater than about 100 m.sup.2/gm, preferably greater than 500 m.sup.2/gm, and most preferably greater than 1000 m.sup.2/gm. Also disclosed is a capacitor that includes at least an electrode comprising such a meso-porous nanocomposite material. A supercapacitor featuring such a nanocomposite exhibits an exceptionally high capacitance value.