To expand an operation region in which desulfurization treatment of a NOx storage reduction catalyst can be done by surely providing an oxygen deficient condition while controlling the temperature of a catalyst bed of the NOx storage reduction catalyst to an appropriate desulfurization temperature condition.

Main flow of exhaust gas 3 is distributed alternately to a pair of NOx storage reduction catalysts 5A, 5B installed in parallel in a middle of an exhaust pipe 4. Fuel addition to the NOx storage reduction catalyst 5B or 5A to which the main flow of exhaust gas 3 is distributed is intermittently executed to retain temperature of the catalyst bed in the desulfurization temperature condition. Fuel addition to the NOx storage reduction catalyst 5A or 5B to which the main flow of exhaust gas 3 is shut off is intermittently executed to provide an oxygen deficient condition in a surrounding atmosphere.

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