NOVELTY - The lithium-ion secondary battery comprises positive and negative electrodes, a separator element, an electrical conductor element, and a binder. The positive electrode comprises a lithium-containing metal phosphate compound (2) coated with a carbon material having a graphene phase and an amorphous phase, a carbon black(4), and a fibrous carbon material (5). The negative-electrode material comprises a graphite carbon material having a carbon phase consisting of a graphene phase and an amorphous phase, a carbon black, and a fibrous carbon material.    USE - The lithium-ion secondary battery is useful in automotives such as electric vehicles and hybrid cars and portable electronic devices.    ADVANTAGE - The safe and cost-effective lithium-ion secondary battery exhibits good capacity and energy density, high electrochemical performance, and long service life so the car can be traveled to a long distance and consumes a minimal amount of fuel.    DETAILED DESCRIPTION - The lithium-ion secondary battery comprises positive and negative electrodes, a separator element, an electrical conductor element, and a binder. The positive electrode comprises a lithium-containing metal phosphate compound (2) coated with a carbon material having a graphene phase and an amorphous phase, a carbon black(4), and a fibrous carbon material (5). The negative-electrode material comprises a graphite carbon material having a carbon phase consisting a graphene phase and an amorphous phase, a carbon black, and a fibrous carbon material. The binder comprises a water-soluble synthetic resin or a water-dispersible synthetic resin. The carbon black is a conductive carbon black including acetylene black and Ketjen black. The fibrous carbon material is a carbon nanotube and/or a carbon nanofiber, and a mixture of a fibrous carbon material (5a) having a small fiber diameter and a short fiber length and a fibrous carbon material (5b) having a large fiber diameter and a long fiber length. The fibrous carbon material having a small fiber diameter and a short fiber length is mainly present on the surface of the lithium-containing metal phosphate particulates, and the fibrous carbon material having a large fiber diameter and a long fiber length is mainly present between the lithium-containing metal phosphate particulates. The graphite carbon is artificial graphite or graphitazable powder. The binder comprises a binder dispersant and s surface active agent. The surface active agent is a polar solvent. An amount of the surface active agent is present in amount of 0.5-5 mass%. A thickness of the coating layer is 2-5 nm. A diameter fiber of a first fibrous carbon material is 10 nm, and a diameter of a second fibrous carbon material is 100 nm. A fiber length of the first fibrous carbon material is 3 mu m, and a fiber length of the second fibrous carbon material is 5 mu m. A ratio of a total content of the carbon black and the fibrous carbon material to a total content of the coated lithium-containing metal phosphate compound is 2-10 mass% in the positive electrode. A ratio of a total content of the carbon black and the fibrous carbon material to a total content of the coated graphite carbon material is 2-10 in the negative electrode. The electronic conduction occurs between a surface of the graphene phase or the amorphous phase, a surface of the carbon black and a surface of the fibrous carbon material, due to compositeness resulting from bonds between carbon atoms. An INDEPENDENT CLAIM is included for a method of producing a lithium-ion secondary battery.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic view of a positive-electrode material for a lithium-ion secondary battery.    Lithium-containing metal phosphate compound (2)    Carbon black (4)    Fibrous carbon material (5)    Fibrous carbon material having a small fiber diameter and a short fiber length (5a)    Fibrous carbon material having a large fiber diameter and a long fiber length. (5b)