Single conical nanopores were fabricated by etching single-ion-irradiated polymer (ethylene terephthalate) (PET) films. The etching process was monitored by measuring the transmembrane current. A series of conical nanopores with different tip sizes were obtained at different maximum etching currents, "Imax". Results showed that it was possible to control the tip diameter by terminating etching at a certain Imax. The current-voltage characteristic of the nanopores in KCl solution was investigated. Results showed also that the ionic conduction was asymmetrical, this phenomenon is called rectification. The current rectification coefficient, was influenced by the tip size and electrolyte concentration.