Abstract: A turbo-supercharger for an engine includes a turbine casing having a turbine scroll divided into a first and second inlet passages. The inlet passages are opened to the engine exhaust passage through first and second inlet ports formed in a mating surface where the turbine casing is attached to the exhaust passage. A shut-off valve is provided in the exhaust passage and has a valve member which is adapted to be seated on the mating surface to close the second inlet port to thereby allow the exhaust gas to flow only through the first inlet passage. The shut-off valve is opened under high speed, heavy load operation so that the exhaust gas is passed through both the first and second inlet passages. A bypass passage is provided in the turbine casing to open at one end to the first inlet passage. A waste gate valve is provided to open the bypass passage when the supercharging pressure exceeds a predetermined value.