An abnormality-determining device for a turbo-supercharger, which is capable of detecting abnormalities, including response delay of a movable member, with accuracy. A turbo-supercharger provided in an internal combustion engine has variable vanes 8c arranged in an exhaust turbine, for changing an area of a nozzle thereof. An abnormality-determining device stops supply of fuel to the engine, when the engine is in a predetermined operating condition, actuates the variable vanes, after actuating the same toward one of an open side and a closed side, toward the other of the sides, during the stoppage of fuel supply, detects a supercharging parameter indicative of a degree of supercharging by the turbo-supercharger, and determines abnormality of the turbo-supercharger based on a change in the supercharging parameter detected during the actuation of the movable vanes.