Provided is a method of producing an integral 3D graphene-carbon hybrid foam, comprising: (a) mixing multiple particles of a graphitic material and multiple particles of a solid polymer carrier material to form a mixture in an impacting chamber of an energy impacting apparatus; (b) operating the energy impacting apparatus to peel off graphene sheets from the graphitic material and transferring the graphene sheets to surfaces of solid polymer carrier material particles to produce graphene-coated polymer particles; (c) recovering the graphene-coated polymer particles from the impacting chamber and consolidating the graphene-coated polymer particles into a desired shape of graphene-polymer composite structure; and (d) pyrolyzing the shape of graphene-polymer composite structure to thermally convert the polymer into carbon or graphite that bonds the graphene sheets to form the integral 3D graphene-carbon hybrid foam.