Provided is method of producing a porous anode material structure for a lithium-ion battery, the method comprising (A) providing an integral 3D graphene-carbon hybrid foam comprising multiple pores, having a pore volume Vp, and pore walls; and (B) impregnating or infiltrating the pores with a fluid for forming a coating of an anode active material, having a coating volume Vc, deposited on or bonded to surfaces of the 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 1/200 to 1/2, and wherein the volume ratio Vp/Vc is from 0.1/1.0 to 10/1.0.