In the literature, conventional electrokinetics is widely used as a principle of operating nanofluidic devices. Different from the conventional electrokinetics involving nonpolarizable solid surfaces with fixed surface charge, induced-charge electrokinetic (ICEK) phenomena deal with polarizable surfaces with the ability of surface charge modulation through electric polarization under external electric fields. Because of several advantages, ICEK phenomena have drawn a great deal of attention in microfluidic community. Herein, we propose the first effort of extending the ICEK phenomena from microfluidics to nanofluidics. In particular, we report a numerical model for the ICEK phenomena in a tapered nanochannel with conducting (ideally polarizable) walls. It is shown that due to the broken geometric symmetry of the nanochannel, induced-charge electroosmotic flow inside the nanochannel exhibits a flow rectification such that electrolyte solution always flows from the narrow end of the nanochannel to the wide end for either a forward electric bias (electric field from the narrow to wide ends) or a reverse electric bias (electric field from the wide to narrow ends). In addition, we demonstrate that the ion selectivity of such tapered conducting nanochannel can be actively tuned to be cation-selective with a forward bias and anion-selective with a reverse bias. Promisingly, conducting nanochannels with broken geometric symmetry could be potentially used for constructing nanofluidic pumps with the unidirectional pumping capacity and ion selectors with the tuneable ionic selection.