In order to prevent the generation of surge noise or other abnormal phenomena during deceleration of a vehicle, the present engine control apparatus comprises a turbo-supercharger driven by exhaust energy of the engine, at least one of an NO.sub.x trap catalyzer and a DPF mounted in the exhaust path of the engine for purifying the exhaust, an EGR path interconnecting the exhaust path and the inlet path of the engine, an EGR valve for adjusting the cross-section of the duct of the EGR path, means for detecting deceleration, and a fuel cutoff control means that, if predetermined conditions are satisfied, effects fuel cutoff control to reduces the rate of fuel injection, wherein the EGR valve is closed during the period of vehicle deceleration.