In this paper, we present a model predictive controller for the autonomous vehicle lane-change maneuver. Firstly, an optimal trajectory is generated by polynomial, then, utilize it as the reference trajectory of the controller. It is well known that vehicle with nonholonomic constraints can not be feedback stabilized through continuously differentiable, time-invariant control laws. One of the advantages of MPC is the ability to handle constraints in a straightforward way. Quadratic programming is used to solve a linear MPC by successive linearization of an error model of the vehicle. Due to that the vehicle dynamics model is used, in order to prevent optimal solution cannot be obtained within the prescribed time, the relaxation factor in the objective function.