The development of new rechargeable battery systems could fuel various energy applications, from personal electronics to grid storage. Rechargeable aluminium-based batteries offer the possibilities of low cost and low flammability, together with three-electron-redox properties leading to high capacity. However, research efforts over the past 30 years have encountered numerous problems, such as cathode material disintegration, low cell discharge voltage (about 0.55 volts; ref. 5), capacitive behaviour without discharge voltage plateaus (1.1-0.2 volts or 1.8-0.8 volts) and insufficient cycle life (less than 100 cycles) with rapid capacity decay (by 26-85 per cent over 100 cycles). Here we present a rechargeable aluminium battery with high-rate capability that uses an aluminium metal anode and a three-dimensional graphitic-foam cathode. The battery operates through the electrochemical deposition and dissolution of aluminium at the anode, and intercalation/de-intercalation of chloroaluminate anions in the graphite, using a non-flammable ionic liquid electrolyte. The cell exhibits well-defined discharge voltage plateaus near 2 volts, a specific capacity of about 70 mA h g(-1) and a Coulombic efficiency of approximately 98 per cent. The cathode was found to enable fast anion diffusion and intercalation, affording charging times of around one minute with a current density of ~4,000 mA g(-1) (equivalent to ~3,000 W kg(-1)), and to withstand more than 7,500 cycles without capacity decay.