This paper presents a cooperative shared control driver assistance system which supports the driver in the longitudinal vehicle control. The system architecture design enables the driver and the assistance system to apply a force on the accelerator pedal. Therefore, a cooperative control algorithm has to be developed. This design problem can be described mathematically as a differential game. For this approach, a model of the driver and the longitudinal vehicle dynamics is necessary. On this basis, the controller design can be stated as an optimization problem. Since the assistance system design is traced back to an optimization problem, the system is capable to support the driver in various driving situations. To verify if the assistance system is capable to support the driver with vehicle following and velocity control, a driving study on a driving simulator is performed. The results of the study demonstrate that the system can support the participants and improve the performance for the longitudinal vehicle control.