A control device is applied to an engine having a supercharger and a control value. The supercharger contains an opening-area control member that changes an opening-area of an approach zone to a turbine of the supercharger so as to change an amount of energy of the exhaust gas entering into the supercharger. The control valve changes a valve-opening degree so as to change an amount of energy of the exhaust gas entering into the supercharger. At a certain instruction time point, the control device gives an instruction to the control valve so as to change the valve-opening degree by a target difference. At this time point, the control device gives an instruction to the opening-area control member, based on the target difference and a parameter relating to a response-time length of the control valve, so as to change the opening-area of the approach zone.