Control of vehicle platoon can effectively reduce the traffic accidents caused by fatigue driving and misoperation, reduce air resistance by eliminating the inter-vehicle gap which will effectively reduce fuel consumption and exhaust emissions. A hierarchical control scheme for vehicle platoons is proposed in this paper. Considering safety, consistency, and passengers’ comfort, a synchronous distributed model predictive controller is designed as an upper-level controller, in which a constraint guaranteeing string stability is introduced into the involved local optimization problem so as to guarantee that the inter-vehicle gap error gradually attenuates as it propagates downstream. A terminal equality constraint is added to guarantee asymptotic consensus of vehicle platoons. By constructing the vehicle inverse longitudinal dynamics model, a lower-level control scheme with feedforward and feedback controllers is designed to adjust the throttle angle and brake pressure of vehicles. A PID is used as the feedback controller to eliminate the influence of unmodeled dynamics and uncertainties. Finally, the performance of longitudinal tracking with the proposed control scheme is validated by joint simulations with PreScan, CarSim, and Simulink.