Abstract: An internal combustion engine with an apparatus for controlling supercharging pressure. The engine includes at its exhaust pipe a by-pass conduit by-passing a turbine of the supercharger. A by-pass valve (so-called waste gate valve) is arranged in the by-pass conduit, which by-pass valve is connected to a diaphragm type actuator. The actuator has a diaphragm opened to the intake pipe at a position between the compressor of the supercharger and a throttle valve. A fixed orifice is arranged in the conduit. The conduit is at a position between the fixed orifice and the actuator connected to the atmosphere via variable orifice. The orifice is operated in accordance with the engine acceleration condition so that the pressure at which the by-pass valve is opened is increased when the engine is accelerating.