The transport properties of a single-wall ZnO nanotube contacted with two Au (Al or Cu ) electrodes are investigated by a theoretical approach. Our results suggest the contact resistance for ZnO nanotube connected with Au electrodes is the largest one as compared with Al and Cu acting as electrodes. The local density of states (LDOS) near the ZnO nanotube/Cu(Al) interface shows the strong electronic interaction. Also shown is that for Au–ZnO system, we can observe a best rectifying performance, the next is the Al–ZnO system, and the third is Cu–ZnO system. This rectification is also fully rationalized by the calculated transmission spectra, the spatial distribution of the lowest unoccupied molecular orbital and highest occupied molecular orbital states, and the electrostatic potential distribution.