With the tight-binding model of semiconductor carbon nanotubes, the third-order nonlinearity of carbon nanotubes has been studied theoretically by using the two-band approximation. Taking the contribution of pure interband transition of pi-electron and has been obtained. The results show that for a typical combined intraband-interband motion into account, a spectrum of chi((3))(THG) semiconductor carbon nanotube the off-resonant magnitude of \chi(THG)((3))\ reaches 10(-7)-10(-8) esu and \chi(THG)((3))\ value at three-photon resonant peak 10(-5) esu. The nonlinear susceptibility chi(THG)((3)) strongly depends on the nanotubes geometry and considerably increases with the increasing radii of carbon nanotubes. In addition, it is found that the third-order nonlinear susceptibility of carbon nanotubes obeys 1/Delta(g)(6) law. (C) 2004 Elsevier B.V. All rights reserved.