In this work, conduction mechanisms of Al/anodic Al oxide/ Al structure, which exhibits resistive switching behavior, have been investigated. The low-resistance state shows ohmic conduction with a metal-like behavior similar to that of pure aluminum. The situation can be explained by the existence of the metallic filament formed by the excess Al in the Al oxide. On the other hand, the high-resistance state (HRS) shows two distinct regimes: ohmic conduction at low fields with a semiconductor-like behavior; and a non-ohmic conduction at high fields. The ohmic conduction of HRS at low fields is attributed to the electron hopping between the states in the oxide with the activation energy of $0.23 eV. It is suggested that the conduction of HRS at high fields (the maximum voltage is lower than the set voltage) is due to the field-enhanced thermal excitation of the electrons trapped in the states of the metallic Al nano-phase into the conduction band of the Al oxide or the electron emission from the potential well of the metallic Al nano-phase to the conduction band. V