PROBLEM TO BE SOLVED: To properly maintain the efficiency, etc., of a supercharger, by effectively and cooperatively controlling an exhaust reflux valve and a supercharger in an operation region being performing an exhaust reflux. SOLUTION: A device, equipping a turbo-supercharger and an EGR device, and also having a means for controlling an EGR valve so as to equate an air- fuel ratio with a target air-fuel ratio; is equipped with a suction pressure sensors 24 for detecting supercharging pressure, an air flow sensor 33 for detecting fresh air quantity to an engine, and a controlling means 40. The means 40 controls at least one side of the driving quantity of the turbo-supercharger and the opening quantity of the EGR valve, so that the supercharging pressure and the fresh air quantity can be increased/decreased in accordance with each other, following the change of an operation condition in an operation region making exhaust reflux.