In preceding vehicle following control apparatus and method for an automotive vehicle, a vehicular velocity controller includes a target inter-vehicle distance calculating section that calculates a target inter-vehicle distance from the vehicle to a preceding vehicle detected by an inter-vehicle distance sensor on the basis of a vehicular velocity detected by a vehicular velocity detector and an inter-vehicle distance detected by an inter-vehicle distance detector, a first vehicular velocity controlling section that performs a vehicular velocity control to bring the detected inter-vehicle distance substantially coincident with the target inter-vehicle distance, and a vehicular deceleration stopping section that performs a vehicular deceleration control to stop the vehicle in accordance with the inter-vehicle distance from the vehicle to the preceding vehicle immediately before a time point at which the inter-vehicle distance detector which trapped the presence of the preceding vehicle has not detected the preceding vehicle when the detected vehicular velocity falls in a low vehicular velocity region lower than a predetermined velocity value and -the inter-vehicle distance detector which trapped the presence of the preceding vehicle has not detected the preceding vehicle.