In an inter-vehicle distance control apparatus and an inter-vehicle distance control method, object detection information is obtained from a detection portion that detects a first preceding vehicle ahead of a vehicle, and an object ahead of the first preceding vehicle; a first possible target stop position is calculated taking into account the first preceding vehicle, and a second possible target stop position is calculated taking into account the object, based on the object detection information; and a target stop position for the vehicle is set to one of the first possible target stop position and the second possible target stop position, which is closer to the vehicle than the other of the first possible target stop position and the second possible target stop position is.