A lithium-air battery is provided, which includes a cathode having a gas diffusion layer containing a solid electronically conductive material coated with carbon black, the gas diffusion layer being at least partially filled with gaseous air, a separator having an electronically nonconducting filter material arranged between the anode and the cathode, the filter material being at least partially impregnated with a liquid electrolyte, and an anode containing a material selected from lithium metal, material alloyable with lithium, metal oxide, and mixtures thereof. Methods for making such battery and the use of such battery in a motor vehicle are also provided.