Here we propose the use of a carbon material called graphene-like-graphite (GLG) as anode material of lithium ion batteries that delivers a high capacity of 608 mAh/g and provides superior rate capability. The morphology and crystal structure of GLG are quite similar to those of graphite, which is currently used as the anode material of lithium ion batteries. Therefore, it is expected to be used in the same manner of conventional graphite materials to fabricate the cells. Based on the data obtained from various spectroscopic techniques, we propose a structural GLG model in which nanopores and pairs of C-O-C units are introduced within the carbon layers stacked with three-dimensional regularity. Three types of highly ionic lithium ions are found in fully charged GLG and stored between its layers. The oxygen atoms introduced within the carbon layers seem to play an important role in accommodating a large amount of lithium ions in GLG. Moreover, the large increase in the interlayer spacing observed for fully charged GLG is ascribed to the migration of oxygen atoms within the carbon layer introduced in the state of C-O-C to the interlayer space maintaining one of the C-O bonds.