  The ground-state properties of the three-leg S=3/2 Heisenberg tube are
studied using the density-matrix renormalization group method. We find that the
spin-excitation gap associated with a spontaneous dimerization opens for the
whole coupling regime, as seen in the three-leg S=1/2 Heisenberg tube. However,
in contrast to the case of S=1/2 tube, the gap increases very slowly with
increasing the rung coupling and its size is only a few % or less of the leg
exchange interaction in the weak- and intermediate-coupling regimes. We thus
argue that, unless the rung coupling is substantially larger than the leg
coupling, the gap may be quite hard to be observed experimentally. We also
calcuate the quantized Berry phase to show that there exist three kinds of
valence-bond-solid states depending on the ratio of leg and rung couplings.
