Autonomous vehicle have the potencial to change the ways of mobility and transportation in the world. Because of today's transportation importance, this technology is placed on the top of initiators of a new industry revolution. This makes this area of technology desirable as a master's thesis. In this thesis, a control system for trajectory tracking that replicates a behavior of an autonomous vehicle is designed in Matlab/Simulink program enviroment . The model of the autonomous vehicle consists of two parts: a model of lateral dynamics and a model of longitudinal dynamics. For the model of lateral dynamics a model predictive controller has been designed and for the model of longitudinal dynamics an open loop system has been set. Model predictive control is a strong optimization control strategy which, because of it's possibilities of solving a desired optimization problem within set limitations, represents one of the most advanced modern control methods. Beside the vehicle, in the Matlab enviroment, the driving scenario consists of a road on which the vehicle is driving and a sensor, placed on the vehicle, that reports data interpreted as a reference for the corresponding controller. Last part of the thesis demonstrates the obtained results and comments with what actions could the autonomous driving system be improved.