Tight-binding molecular dynamics was used to simulate the thermal behavior of carbon nanotubes （CNTs） in this paper. A few kinds of single wall CNTs （SWCNTs） and double wall CNTs （DWCNTs） were studied during the simulation experiment at temperatures of 300—4000 K and the pressure of 1 atm. The results showed that the chiral SWCNTs have higher thermally stability than the armchair and zigzag type, and that the bigger the nanotube diameter is, the more stable the nanotube stucture is for those with the same chiral angles. The DWCNTs with at least one chiral structured wall are more stable than the others, but that with two zigzag walls were damaged badly, which also gives support to the study about SWCNT thermo-stability. One factor to describe CNTs in connection with their thermo-stability was proposed, and some data were theoretically analyzed based on carbon bond structures.