An engine turbo-supercharger including an exhaust gas turbine provided in the exhaust gas passage of an engine, a compressor provided in the intake passage of the engine and adapted to be driven by the turbine, a variable nozzle being provided in the exhaust gas passage upstream the turbine for changing an effective area of the exhaust gas passage leading to the turbine. The variable nozzle has a first position wherein a smaller effective passage area is provided and a second position wherein a larger effective passage area is provided, a bypass passage being provided in the exhaust gas passage and bypassing the turbine, a bypass valve for opening the bypass passage when the intake pressure of the engine increases beyond a predetermined value so that the intake pressure is maintained below the predetermined value. An engine intake gas flow detecting device is provided for detecting a physical value relating to the engine intake gas flow, a control circuit for detecting an engine operating condition wherein the engine intake pressure becomes the predetermined value when the variable nozzle is in the second position and moving the variable nozzle to the second position when the engine operating condition is detected.