At this moment a revolution is going on in the development of our vehicles. The driver is going to be replaced by the vehicle itself. To investigate this autonomy Delft University of Technology (TU Delft) is project leader of a partnership called Dutch Automated Vehicle Initiative (DAVI). This group of industry and academics are combining their efforts in development and implementation of autonomous driving systems. The aims of the initiative is to investigate, improve and demonstrate automated driving on public roads. One of the DAVI projects the TU Delft is currently working on is the development of an autonomous vehicle. This autonomous vehicle is designed in different stages with different systems. Apart from observing the surroundings of the autonomous vehicle and planning a trajectory it is also required to have a system that is capable of controlling the movement of the vehicle. In this thesis such a system will be developed for the Toyota Prius of the DAVI project. In contradiction to most Advanced Driving Assist Systems (ADAS) the developed system does not follow another vehicle, but instead it follows a trajectory that is represented as a list of path points. As part of this design a suitable vehicle model is selected with use of literature. Because this system will be based on the Toyota Prius it was required to find the vehicle model parameters from the actual vehicle. This is done with use of measurements and optimisation. The path following system was split into two control parts, lateral controller for steering and a longitudinal controller for acceleration. These controllers are designed with the aim of real implementation via LabVIEW from National Instruments. Therefore the real-time capabilities are discussed. The control algorithms are selected based on the expected requirements for computational power. After the construction of the path follower system in LabVIEW the performance was tested with use of simulations. The tuning of the controller was investigated and the best performing control parameters were found. Then the system was implemented into the real vehicle and tests were conducted to see the difference between simulation and real world. The results of these tests were then evaluated. The distance error between the vehicle and the path was in the real test within $15.8 cm$. It was proven that the system is able to perform in real-time with a satisfying performance in terms of stability, comfort and trajectory tracking.