PURPOSE: To aim at enhancing the supercharging effect in a low rotational speed range by selectively introducing a boost pressure, first and second air pressures into a pressure chamber in an actuator for a waste gate valve.

CONSTITUTION: A boost pressure downstream of a compressor 22 and air pressures from first and second air pressure sources 58, 60 are selectively led into a pressure chamber 36 in an actuator 32 for a waste gate valve 30. That is, the boost pressure is fed at a rotational speed less than a first predetermined rotational speed, but the first air pressure is fed at a speed higher than the first predetermined rotational speed but lower than a second predetermined rotational speed while the second air pressure which is higher than the first air pressure is fed at a speed higher than the second predetermined rotational speed. With this arrangement, the waste gate valve is held in a fully closed condition in a low rotational speed range, thereby it is possible to enhance the charge effect.