The Li absorption energies of single-walled armchair (6,6) and zigzag (12,0) carbon nanotubes are investigated by the first-principles molecular orbital methods. It is found that Li can be absorbed inside as well as outside these carbon nanotubes with the approximately similar absorption energy. It is still energetically favorable for Li to be absorbed both inside and outside carbon nanotubes. Furthermore, it is shown that the Li absorption weakens the covalent C-C bond, but instead forms the ionic Li-C bond which works to stabilize the Li carbon nanotube material.