A lithium-air battery includes a lithium negative electrode, a positive electrode including a catalyst containing gold, and a non-aqueous electrolyte interposed between the positive electrode and the lithium negative electrode. The catalyst includes gold supported on a cerium-containing oxide, such as a cerium-zirconium compound oxide or a cerium-aluminum compound oxide. The amount of catalyst of the positive electrode is in the range of 0.01 to 50 weight percent relative to the total weight of the positive electrode.