the invention relates to a constant - speed cruise control apparatus for automatically controlling the cruise speed of a vehicle to permit the vehicle to cruise at a constant speed . the gradient of a road is estimated on the basis of an actual cruise speed of the vehicle , the opening of a throttle valve , and cruise performance characteristics of the vehicle which indicates the relationship between the cruise speed and the opening of a throttle valve . if it determines that the road is uphill , and moreover , the absolute value of a speed deviation is more than a predetermined value , shifting down is carried out . subsequently , if the absolute value of the speed deviation is less than another predetermined value , and moreover , it is determined that the road is downhill , shifting up is carried out . through such shift - up and shift - down control on the basis of both the speed deviation and the road gradient , it is possible to perform speed change control according to the conditions of the surface of a road , thereby carrying out a highly reliable constant speed cruise of the vehicle .