In order to prevent a catalyst for an internal combustion engine from experiencing decreased efficiency by deterioration after long time use of the catalyst, the decreased efficiency of the catalyst is determined, and the internal engine is controlled based on results of the determination so as to maintain high efficiency of the catalyst. The catalyst is installed in an exhaust pipe of the engine. Sensors for detecting conditions of exhaust gas both at a upstream side and a downstream side of the catalyst are provided, respectively. As for the sensor, for example, an oxygen sensor whose output varies stepwise at .lambda.=1, or a sensor whose output varies in proportion to air-fuel ratio can be used. Detected values of the sensors are taken into a control unit, catalyst efficiency and deteriorating degree of the catalyst are estimated by comparison of the detected values, and the engine is controlled so that the catalyst efficiency is maximized. A preferable exhaust gas cleaning characteristics of the catalyst can be maintained because the decreased efficiency of the catalyst is determined exactly and the engine is controlled so as to prevent the catalyst from experiencing decrease efficiency.