The speed of a vehicle is automatically controlled in a speed bump area located in the vicinity of a speed bump. Information about a speed bump is received from a navigation device, and a distance between the vehicle and the speed bump is calculated. If the calculated is less than a preset reference distance, it is determined that the vehicle is entering or has entered an area of the speed bump. Upon determining that the vehicle is in the speed bump area, a speed difference between a safe speed bump crossing speed and a current speed of the vehicle is computed, a required acceleration value is calculated based on the calculated distance to the speed bump and the speed difference, and the speed of the vehicle is controlled so that the vehicle decelerates or accelerates in accordance with the required acceleration value.