Abstract: An engine is provided with a primary turbocharger and a secondary turbocharger having blowers disposed in the intake passage of the engine in parallel to each other and turbines disposed in the exhaust passage of the engine in parallel to each other. An exhaust cutoff valve disposed in the exhaust passage opens to feed exhaust gas to the turbine of the secondary turbocharger to operate the secondary turbocharger only in a large intake air mass range. A waste gate valve opens to relieve exhaust gas fed to the turbochargers when the supercharging pressure exceeds a predetermined value. The waste gate valve is kept closed for a predetermined time after the operating condition of the engine shifts into the large intake air mass range and the exhaust cutoff valve opens when shift of the operating condition of the engine from a small intake air mass range to the large intake air mass range is required.