We present molecular dynamics study of a generic (coarse-grained) model for single-polymer diffusion confined in a corrugated cylinder. For a narrow tube, i.e., diameter of the cylinder δ < 2.3, the axial diffusion coefficient D|| scales as D|| ∝ N−3/2, with chain length N, up to N ≈ 100 and then crosses over to Rouse scaling for the larger N values. The N−3/2 scaling is due to the large fluctuation of the polymer chain along its fully stretched equilibrium conformation. The stronger scaling, namely N−3/2, is not observed for an atomistically smooth tube and/or for a cylinder with larger diameter.