PURPOSE: To provide a method for purifying exhaust gas which reduces catalyst poisoning by SOx contained in exhaust gas and at the same time controls H2S releasing into the air.

CONSTITUTION: When an upstream side catalyst converter CA-1 and a downstream side catalyst converter CA-2, which are installed in an exhaust duct line of an engine 2, are in a warming condition, an air fuel ratio perturbation is conducted in which the air fuel ratio is temporarily changed alternately between a rich region and a lean region on the basis of a theoretical air fuel ratio. When the catalyst converter CA-1 is in a rich atmosphere, SOx stored in the converter CA-1 is reduced into H2S, and the H2S is released from the converter CA-1. In this way, the poisoning of the converter CA-1 by SOx is reduced. Next, the capture of released H2S and the oxidation of the released H2S are conducted on the converter CA-2 side, reducing H2S releasing into the air.