Dependence of the thermal conductivity on the length of two armchair single-walled carbon nanotubes (SWNTs) is studied by the nonequilibrium molecular dynamics (MD) method with Brenner Ⅱ potential. The thermal conductivities are calculated for (5, 5) and (7, 7) SWNTs with lengths ranging from 22 to 155 nm. The results show that the thermal conductivity of SWNTs is sensitive to the length and it does not converge to a Unite value when the tube length increases up to 155 nm, however it obeys a power law relation.