This apparatus determines that a driver demands the maintenance of a vehicle body speed from a cancel operation (ON.fwdarw.OFF) of an acceleration requiring operation by an accelerator pedal or a cancel operation (ON.fwdarw.OFF) of a deceleration requiring operation by a brake pedal BP, so that it detects a "body-speed-maintenance requiring operation" (at time t1), and stores the vehicle body speed Vso at the point of the detection as a "required maintenance vehicle speed Vref". When the apparatus determines that the vehicle is on a downhill after the detection of the "body-speed-maintenance requiring operation" (time t2), it feedback-controls the brake hydraulic pressure Pw to thereby start and execute the automatic control (downhill speed control) of the vehicle body speed Vso such that the vehicle body speed Vso is maintained at the required maintenance vehicle speed Vref.