A coaxial cylindrical heterojunction of carbon tubes, which consists of alternant bands of 5- and 7-membered rings, can be formed by one armchair (n, n) carbon nanotube and one zigzag (2n, 0) carbon nanotube. The torsional mechanical properties of this kind of (n, n)-(2n, 0) heterojunction constructed by the same length of armchair and zigzag nanotubes are studied by using molecular dynamics method. In order to make a comparison, the relations of the torque and axial stress to torsional angle of (n, n) and (2n, 0) carbon tubes are also systemically calculated. Moreover, the transfer process of torsional stress in the (n, n)-(2n, 0) heterojunction is analyzed. Some important conclusions are obtained. Firstly, the torsional angle corresponding to the buckling point of carbon nanotubes is closely related to their torsional stiffness. The buckling angle decreases monotonically with torsional stiffness. Secondly, as the torsion develops, the torsional stress appears from the joint position due to the fact that the junction part in the (n, n)-(2n, 0) heterojunction has the smallest torsional stiffness and then transfers from the joint position to both ends. The propagation velocity of the torsional stress in (n, n) nanotube which has smaller stiffness is faster than that in (2n, 0) nanotube with bigger stiffness. Finally, for the process of torsion within the elastic limit, no axial stress is produced in (n, n)-(2n, 0) heterojunction during the torsion. This effect is of great significance for designing the carbon nanotube-based nano-oscillator devices.