Motion of single-walled carbon nanotubes on graphite substrate is investigated by using molecular dynamics simulation in this paper. Following a relaxation to the equilibrium state, a uniform force is applied to carbon nanotubes for a period of time to set them into motion. After the applied force being removed, carbon nanotubes move relative to the substrate in decelerating speed until they come to a full rest in the end. Different tube radius and chiral angles are selected during simulation. The results show that motion of carbon nanotubes is mainly affected by the chiral angle but independent of tube radius. When the chiral angle is 30°, periodic transition between sliding and rolling is observed due to the periodic change of atomic configuration during the motion. When chiral angle is between 28.3° and 30°, sliding and rotating take place at the same time. When chiral angle is less than 26.3°, only sliding is observed. Different chiral angles result in different atomic configurations in the contact region between carbon nanotubes and graphite substrate, which gives rise to different styles of motion.