The diffusion of polymer in long cylindrical tubes is investigated by using Monte Carlo simulations. Two kinds of cylindrical tubes are taken into account: (1) a homogeneous tube where the polymer-tube interaction is independent of monomer position along the longitudinal direction of the tube, and (2) a periodic one where the interaction is periodically changed along the tube. In the homogeneous tube, the diffusion coefficient along the longitudinal direction decreases with the decrease in the tube radius and decreases with the increase in the polymer-tube interaction. While in the periodic tube, the diffusion coefficient is further influenced by period length of potential. We find that the diffusion coefficient changes non-monotonically with the period length and the result can be attributed to the competition between polymer statistical size and period length of potential. The diffusion coefficient is relatively high when polymer size roughly matches the period length or when polymer size is much larger than the period length. (C) 2016 Elsevier Ltd. All rights reserved.