a b s t r a c tWhile the speculation that graphene may owe double or even higher capacity of lithium adsorption than graphite does remains speculative, there is growing evidence that defects and edges may promote lithium adsorption on graphene and other nanostructured carbon. Here we report a first-principles study on how grain boundary defects in graphene may influence the adsorption of lithium. The adsorption energy for Li atoms trapping in 5-, 7-, and 8-rings is much lower than the counter-part of Li atoms and pristine graphene. Such defective graphene could adsorb more Li atoms, and may reach the speculated ratio of 1:1 for C-Li adsorption. In a contrast study of lithium on fullerenes of different size, we find that the adsorption energy decreases with increasing size of fullerenes, but does not approach the energy when Li atoms adsorb on flat graphene. The energy in carbon nanotubes, however, converges to the adsorption energy between Li atoms and flat graphene if the radius of carbon nanotubes is sufficiently large. It hence indicates that while curvature plays a role in the enhanced adsorption in fullerenes, the twelve 5 rings in a fullerene ball is the primary factor accounting for the enhanced lithium adsorption.