A control system includes a supercharged engine and an electronic control unit. The supercharged engine includes an exhaust passage, a turbine, and an exhaust catalyst. The turbine includes a turbine control valve. The electronic control unit is configured to calculate (S103) a first exhaust gas temperature and a second exhaust gas temperature that are temperatures of exhaust gas flowing into the exhaust catalyst. The electronic control unit is configured to control the turbine control valve such that: the turbine control valve is set to the first valve opening degree (S104, S105) when the first exhaust gas temperature is higher than the second exhaust gas temperature; and that the turbine control valve is set to the second valve opening degree (S104, S106) when the second exhaust gas temperature is higher than the first exhaust gas temperature.