Nonresonant enhancements of third-order susceptibility χ(3)(-ω; ω, ω, -ω) have been investigated for zigzag carbon nanotube (n,0) bundles (n = 5, 7, 11, 13, 8, 10, 14, 16) based on the energy band theory combined with the classic anharmonic oscillator model. The obtained results show that the (3) values increase as circumference of tube varies in the order of 5<7<11<13 and 8<10<14<16 for (n,0) tube bundles, respectively. The origination of the large third-order susceptibility is ascribed to the circumference effect of individual tube. The nonresonant third-order susceptibility is estimated to be about 10-6 esu in the axial direction of (16,0) tube bundles, and it is possible for a good candidate to make optical phase conjugate device.