An apparatus for purifying an exhaust gas emitted from an internal combustion engine, particularly, immediately after starting of the engine, includes a mechanism for reducing the time required to heat a catalyst converter to the activation temperature. The exhaust gas is passed through a preliminary catalyst close to the engine and then through a main catalyst downstream of the catalyst. The engine is operated with an air-fuel mixture which is richer than the amount indicated by the stoichiometric air/fuel ratio for a period of time from when engine is started until the main catalyst is heated to a temperature at which the catalyst can sufficiently perform its purifying capability. The preliminary catalyst is enabled to function at lower temperatures by combusting the exhaust gas which is generated during a rich air-fuel mixture condition. The main catalyst can be heated with the generated combustion heat, resulting in an enhancement in exhaust gas purifying capability.