Provided is a supercapacitor having an anode, a cathode, a porous separator/electrolyte, wherein at least one of electrodes contains an integral 3D graphene-carbon hybrid foam composed of multiple pores and pore walls, wherein the pore walls contain single-layer or few-layer graphene sheets chemically bonded by a carbon material having a carbon material-to-graphene weight ratio from 1/100 to 1/2, wherein the few-layer graphene sheets have 2-10 layers of stacked graphene planes having an inter-plane spacing d002 from 0.3354 nm to 0.40 nm and the graphene sheets contain a pristine graphene material having essentially zero % of non-carbon elements, or a non-pristine graphene material having 0.01% to 25% by weight of non-carbon elements wherein said non-pristine graphene is selected from graphene oxide, reduced graphene oxide, graphene fluoride, graphene chloride, graphene bromide, graphene iodide, hydrogenated graphene, nitrogenated graphene, doped graphene, chemically functionalized graphene, or a combination thereof.