Although dominating the consumer electronics markets as the power source of choice for popular portable devices, the common lithium battery is not yet suited for use in sustainable electrified road transport. The development of advanced, higher-energy lithium batteries is essential in the rapid establishment of the electric car market. Owing to its exceptionally high energy potentiality, the lithium-air battery is a very appealing candidate for fulfilling this role. However, the performance of such batteries has been limited to only a few charge-discharge cycles with low rate capability. Here, by choosing a suitable stable electrolyte and appropriate cell design, we demonstrate a lithium-air battery capable of operating over many cycles with capacity and rate values as high as 5,000 mAh g(carbon)(-1) and 3 A g(carbon)(-1), respectively. For this battery we estimate an energy density value that is much higher than those offered by the currently available lithium-ion battery technology.