TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: In the positive electrode: an average particle diameter of the carbonaceous material is 2-900 nm; the nonmetallic element comprises at least one of group 13-16 elements, nitrogen, sulfur, phosphorus, selenium, tellurium or boron; the carbonaceous material is a catalyst (17) that has conductivity, and the catalyst promotes an oxygen reduction reaction and an oxygen evolution reaction; the carbonaceous material is present at 65-99 wt.%; and the non-metallic element is present at 0.1-30 wt.% based on 100 wt.% of the carbonaceous material. The carbonaceous material further comprises: an oxygen reduction catalyst and an oxygen evolution catalyst; a transition metal; and transition metal oxide. The transition metal comprises at least one of cobalt, nickel, iron, gold, silver, platinum, ruthenium, rhodium, osmium, iridium or palladium. The transition metal oxide is oxides of manganese, cobalt, iron, zinc or nickel. The carbonaceous material comprises carbon black, graphite, graphene, activated carbon or carbon fiber. In the method: the non-metal precursor comprises at least one of quinoxaline, hemin, p-toluene sulfonic acid, cobalt-tetramethoxy-phenylporphyrin, iron-tetramethoxy-phenylporphyrin, phthalocyanine, cobalt-phthalocyanine or iron-phthalocyanine; and the slurry further comprises a transition metal precursor. The transition metal precursor comprises at least one of iron(II) nitrate, iron(III) nitrate, iron(II) acetate or iron(III) acetate. A specific surface area of the carbonaceous material doped with the non-metallic element may be measured by performing Brunauer Emmett and Teller analysis and analysis value of the specific surface area is at least 10 m2/g. The mesoporous material is mesoporous silica as a template and the non-metal precursor is attached to the surface of the mesoporous material. EXAMPLE - Iron (III) nitrate (1 g), quinoxaline (3 g) and mesoporous silica template (5 g) were mixed in acetone (4.25 g) and agitated. Then, the mixture was dried at 100 degrees C for 6 hours and then dried at 160 degrees C for 6 hours to remove solvent. Then, heat treatment was performed in nitrogen at 900 degrees C for 3 hours to obtain a product. Then, the product was immersed in hydrogen fluoride (20%) for 4 hours and dried in air for 12 hours to obtain nitrogen-doped mesoporous carbon (particle size of 300 nm) (positive electrode).