PURPOSE: To prevent sudden acceleration or large vehicle-speed overshoot by resetting and then increasing a target vehicle speed when shift-down occurs on a transmission side during acceleration control in which a target vehicle speed is increased at a given acceleration.

CONSTITUTION: A then travel vehicle speed is memorized as a target vehicle speed by turning on a set SW in a constant-speed travel controller 1, thereafter an actuator 3 is driven to open and close a throttle valve 4 until a cancellation signal is inputted, allowing the constant-speed travel control of an engine 6. Turning-on of the accelerator SW during the constant-speed travel control or that of a resumption SW in a cancellation condition causes acceleration control. In this case, the receiving of a shift-down signal from a speed-change controller 2 during acceleration control causes a constant-speed travel controller 1 to make the resetting of a target vehicle speed, and concurrently the speed- change controller 2 to receive a shift-down retention command to prevent speed- change hunting.