The invention belongs to the chemical power supply field, and concretely relates to a high-energy-density Li-air battery air electrode, and a battery and a making method thereof. The air battery is a non-aqueous chargeable Li-air (or Li/O2) battery concretely, and comprises a lithium metal negative electrode, a non-aqueous electrolyte, a diaphragm and the air electrode, the air electrode comprises a catalyst, a carrier and a binder, and the carrier is a composite double pore system material composed of nano-graphene having a two-dimensional nanostructure, a high heat conduction coefficient (-5000W/m.k), a high specific surface area (-2630m<2>/g) and a high electrical conductivity (10<3>-10<4>Sm<-1> and an SiO2 aerogel, provides a circulation channel and a storage space for O2 and discharge reaction products respectively, and adopts a double-surface electrode structure; and the non-aqueous electrolyte adopts a lithium salt and organic solvent mixed electrolyte, and has the advantages of high electrical conduction, low volatility, good chemical stability and the like. The oxygen-selective diaphragm is added to the air battery to increase the pressure of O2 in a reaction area and prevent water in air from entering the battery, so the metallic lithium is effectively protected, and the safety of the battery is increased.