A control system for an internal combustion engine having a compressor wheel and a turbine wheel connected with the compressor wheel and rotationally driven by kinetic energy of exhaust gases from the engine, an exhaust gas flow rate changing device for changing a flow rate of exhaust gases injected to the turbine wheel, an exhaust gas recirculation passage for recirculating the exhaust gases to an intake pipe of the engine, and an exhaust gas recirculation control valve disposed in the exhaust gas recirculation passage. An exhaust pressure is detected, and a value of an intake gas parameter is obtained. A target value of the exhaust pressure and a target value of the intake pipe gas parameter are calculated. A control amount of the exhaust gas flow rate changing device and an opening control amount of the exhaust gas recirculation control valve are calculated using a model predictive control.