A control apparatus for a gas-turbine aeroengine having discriminator that discriminates normality of a low-pressure turbine rotational speed sensor adapted to detect the low-pressure turbine rotational speed and a high-pressure turbine rotational speed controller that establish a first value as an upper limit value of a high-pressure turbine rotational speed and controls the high-pressure turbine rotational speed based on the established upper limit value, and is configured to change the upper limit value to a second value lower than the first value when the low-pressure turbine rotational speed sensor is discriminated not to be normal, whereby engine output (thrust) determined by the low-pressure turbine rotational speed can be controlled to a desired value while restraining the high-pressure turbine rotational speed to not greater than the first value, and low-pressure turbine overspeed at the time of a mishap such as engine fan blade breakage can be reliably prevented.