A lithium ion battery includes a cathode (10) having a plurality of nanoparticles of lithium doped transition metal alloy oxides represented by the formula Li.sub.xCo.sub.yNi.sub.zO.sub.2, an anode (20) having at least one carbon nanotube array (22), an electrolyte, and a membrane (30) separating the anode from the cathode. The carbon nanotube array includes a plurality of multi-walled carbon nanotubes (23). Preferably, an average diameter of an outermost wall of the multi-walled carbon nanotubes is in the range from 10 to 100 nanometers, and a pitch between adjacent multi-walled carbon nanotubes is in the range from 20 to 500 nanometers. In the carbon nanotube array, the lithium ions are able to intercalate not only inside the multi-walled carbon nanotubes, but also in the interstices between adjacent multi-walled carbon nanotubes. Thus a density of intercalation of the carbon nanotube array is significantly higher than that of graphite.