In this paper, ice nanotubes confined in carbon nanotubes are investigated by molecular dynamics. The trigonal, square, pentagonal, and hexagonal water tubes are obtained, respectively. The current-voltage (I-V) curves of water nanotubes are found to be nonlinear, and fluctuations of conductance spectra of these ice nanotubes show that the transport properties of ice nanotubes are quite different from those of bulk materials. Our studies indicate that the conductance gap of ice nanotube is related to the difference value from the Fermi energy EF to the nearest molecular energy level E0. Increasing the diameter of a water molecular nanostructure results in the increase of the conductance.