A control circuit for an air-bag mounted in a motor vehicle comprises an acceleration sensor for producing an acceleration signal indicative of acceleration of the vehicle, an ignition timing circuit for processing the acceleration signal to predict the time when a passenger's head will reach a front surface of the air-bag in fully deployed condition and producing a first air-bag deploying signal in accordance with the predicted time, and a damage discrimination circuit for processing the acceleration signal and judging the need of activation of the air-bag when the cumulative effect of the acceleration exceeds a predetermined limit. The damage discrimination circuit produces a second air-bag deploying signal when judging the need of activation of the air-bag. A so-called AND means is further employed which actually activates the air-bag when receiving the first and second air-bag deploying signals concurrently.