Functional groups and grain boundaries of polycrystalline graphenes play important roles in their tribological behaviors but the mechanism is still elusive. Here, we have investigated the influences of hydroxyl groups, coverage, and grain size on the surface corrugation, friction, and motion behavior of polycrystalline graphene using molecular dynamics simulations. The results show that the corrugation of polycrystalline graphene increases with respect to an increase in grain size. The introduction of hydroxyl groups suppresses the corrugation. The friction between carbon nanotube (CNT) and polycrystalline graphene increases the formation of hydrogen bonds when the interfaces are grafted with hydroxyl groups. The highest amount of friction appears when the ratio of hydroxyl groups on CNT, and polycrystalline graphene, is about 15%-5%. This is due to the balance between the interface space and the formed hydrogen bonds. Furthermore, polycrystalline slides following the movement of CNT owing to high friction. In addition, the energy dissipation as a result of the vibration of the hydroxyl groups plays a more important role as the ratio of hydroxyl groups increases.