1. A following distance control device that controls a vehicle to regulate a distance to a preceding vehicle to a target following distance, the following distance control device comprising: a detecting unit that detects at least one of an acceleration operation and a deceleration operation by a driver; a target following distance changing unit that changes the target following distance on the basis of the acceleration operation or the deceleration operation by the driver that is detected by the detecting unit, wherein after the completion of one of the acceleration operation and the deceleration operation the distance to the preceeding vehicle is regulated according to the target following distance changed by the target following distance changing unit; and an inhibition unit that inhibits a changing amount of the target following distance by the target following distance changing unit when a specified acceleration operation or a specified deceleration operation is executed.