Recent research has demonstrated that cooperative and automated driving functions can improve traffic efficiency and safety. Traffic efficiency can be increased and the overall vehicle energy consumption can be reduced through cooperative driving functions not only on the highway, but also in urban areas. To this end, this paper presents a linear model predictive control (MPC) algorithm for the optimization of velocity trajectories of vehicles in a platoon in an urban traffic environment. A novel centralized approach is implemented to optimize the total energy consumption of all vehicles while improving traffic efficiency. To solve the optimal control problem, for the first time, an additional data‐driven velocity prediction model of the vehicle in front of the platoon is used to consider the influence of realistic prediction errors when evaluating the developed control strategy in a vehicle simulation environment. The simulated total energy consumption is compared with a rule‐based cooperative adaptive cruise control (CACC) algorithm. Furthermore, the traffic density and the platoon string stability, the robustness and computer time of the centralized approach are also included in the evaluation. Simulation results indicate that, considering all evaluation criteria, the centralized cooperative control strategy can improve energy efficiency by up to 15% in the investigated urban scenario.