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To optimize a vehicle platoon system in terms of car-following behavior, a decentralized model predictive control (MPC) strategy for longitudinal velocity control was established (namely, CF-MPC). Firstly, considering the influence of car-following behavior on vehicle states, a longitudinal velocity control model for platoons of connected and automated vehicles (CAV) was designed. Based on that model, an upper-level MPC controller was built to obtain the desired acceleration of the vehicles. Secondly, a lower-level controller received the desired acceleration signal and converted it into the expected throttle opening/braking pressure, to control acceleration/deceleration. Then, the Lyapunov stability method was used to detect the stability conditions that the model should satisfy. Finally, three simulation procedures—constant speed, acceleration, and deceleration were tested, and the validity of the CF-MPC method was verified from the perspectives of a model strategy and a control strategy. The simulation results show that with the proposed CF-MPC method, CAV platoons quickly completed velocity tracking and maintained a safe distance, thereby improving traffic efficiency, fuel economy, driving safety, and transportation capacity.