In automatic following control in a travel control unit of a driving support apparatus, a prerequisite inter-vehicle distance to a front vehicle is set, a time to reaching this requisite inter-vehicle distance is set as a control target time, an estimated position of the front vehicle after the control target time elapses is computed, an acceleration from a present vehicle speed that will bring to a preset target inter-vehicle distance the inter-vehicle distance to the front vehicle at an own vehicle speed as of when the control target time elapses is computed as a target acceleration on the basis of the present inter-vehicle distance to the front vehicle and the estimated position of the front vehicle after the control target time elapses, and automatic braking control and automatic acceleration control are carried out to follow the front vehicle.