Autonomous driving has been a hot topic in both academia and industry since the last millennium. Despite the benefits of driverless cars, it is not strongly supported by the public mainly due to lack of trusts, e.g. no proof on safety, get hacked, or not as smart as humans. Hence, introducing a safety guaranteed control framework for autonomous vehicles is extremely important. An MPC-based approach is introduced, providing a potential framework for rigorous analysis on performance (including safety) of autonomous vehicles. Simulation Studies demonstrate its effectiveness in dynamic environments.