This paper presents a control algorithm for autonomous overtaking problem using stochastic model predictive control. This algorithm relies on suitable prediction for the longitudinal and lateral speeds of the surrounding vehicles. Accordingly, these information are used to formulate suitable dynamics constraints for the proposed control algorithm which determines the need of overtaking action by tracking a suitable longitudinal speed reference and a lateral position reference, while avoiding the obstacles. Finally, the efficiency of the proposed algorithm is illustrated by two traffic scenarios in the environment of the reliable traffic simulator IPG CarMaker.