To provide a reactor for cleaning an exhaust gas, which exhibits high NOX-cleaning performance under a high temperature lean atmosphere.

The reactor for cleaning the exhaust gas is characterized in that an anode is formed on one surface of an oxygen ion conductor, a cathode is formed on the other surface opposed to the surface of the conductor, further an HC-adsorbing layer is formed on the anode, and an electroconductive wire is connected between the anode and the cathode so as to form a closed circuit. It is preferable that a transition metal is used as a constitutive material of the anode and the cathode, and the oxygen ion conductor is constituted of at least one kind of multiple oxide selected from CeO2-Y2O3, CeO2-Gd2O3, CeO2-ZrO2, ZrO2-Y2O3, Bi2O3-Y2O3, La2O3-SrO-Ga2O3-MgO, La2O3-SrO-Ga2O3-MgO- CoO, and BaO-In2O3.