Disclosed are an electrolyte membrane for a lithium-air battery, a method of manufacturing the same, a cathode for a lithium-air battery, a method of manufacturing the same, and a lithium-air battery including the electrolyte membrane and the cathode. Particularly, the lithium-air battery includes i) an electrolyte membrane, which is manufactured using an inorganic melt admixture including two or more nitrogen-oxide compounds and thus may have a very low eutectic point, and ii) a cathode, which is manufactured by reducing a metal at a fast speed on a carbon material. As such, the lithium-air battery is capable of stably operating even at low temperatures and providing high power output.