The paper focuses on the design of a new adaptive cruise control which takes into consideration the knowledge of the inclinations of the road along the track of the vehicle. The controlled system incorporates the brake and the traction forces. By choosing the velocity of the vehicle fitting in with the inclinations of the road the number of unnecessary accelerations and brakes can be reduced, thus so can the operations of the actuators of the vehicles, i.e. the powertrain and the brake system. The longitudinal dynamics of the vehicle is formulated in a control-oriented linear model, which contains the longitudinal control force and disturbances such as the aerodynamic force, rolling resistance and road slope. If the inclination of the road surface is assumed to be known, it is considered in the calculation of the velocity tracking and the reference velocity. In the model the nonlinear properties of the predicted road inclinations are considered together with the safety requirements. The control system is designed by using LPV/H∞ control theory. The operation of the method is demonstrated through simulation examples in Matlab/Simulink and CarSim environments.