The system is provided with a controller that controls the acceleration and deceleration of the vehicle according to the operation quantity of an accelerator pedal, and a state detector that determines whether a wheel is in a slippery state. The controller sets a deceleration region corresponding to a relatively small amount of operation and an acceleration region corresponding to a relatively large operation quantity regarding the operation quantity, and controls such that, in at least partially, the deceleration of the vehicle is increased as the operation quantity decreases, while in at least a part of the acceleration region, the acceleration of the vehicle is increased as the operation quantity increases. When the state detector detects a slippery state, the controller decreases the maximum deceleration that can be produced in the deceleration region.