This paper presents a dynamic collision avoidance controller of a connected vehicle group using Model Predictive Control (MPC). The vehicles should follow a predefined reference trajectory while simultaneously avoiding collisions on this trajectory. MPC pursues the tracking of the reference trajectory in the objective function of the optimization problem. In order to avoid collisions, MPC defines avoidance constraints between each pair of vehicles. Due to the collision avoidance constraints, the feasible set of the optimization problem is non-convex. Thus, the resulting optimization problem is nonconvex. This paper presents an efficient method to solve this non-convex optimization problem based on sequential convex programming.