The thermal conductivity of various carbon nanotubes with defects or intramolecular junctions was studied using nonequilibrium molecular dynamics approach. The results show that the thermal conductivity of both armchair and zigzag carbon nanotubes increased with the decrease of the radius of the tube. The thermal conductivity of armchair tube is higher than that of zigzag tube when the radii of the two tubes are kept almost same. Discontinuities appear on the temperature profile along the tube axial at the region of IMJ, resulting in the large temperature gradient and thus lower thermal conductivity of(n,n)/(m,0)tube with one IMJ and(m,0)/(n,n)/(m,0)tube with two IMJs. For the(m,0)/(n,n)/(m,0)tube with two IMJs, phonon mean free path of the middle(n,n)tube is much smaller than that of the isolate(n,n)tube.