The automotive industry has experienced swift development with the rapid growth of the economy. The increasing number of vehicles has led to deteriorating road traffic conditions, increased consumption of nonrenewable energy, and excessive vehicle emissions. To tackle the problems of fuel efficiency and safety control for vehicle platoons, this study suggests a novel leader-follower optimal control method for vehicle platoons to improve fuel efficiency. Depending on where vehicles are in a platoon, they are classified into two categories: the leader vehicle and follower vehicles. The differing driving circumstances of these two types of vehicles are considered in this paper by using various control methods. On the one hand, the leader vehicle uses an approximate fuel consumption model to improve computational efficiency. At the same time, speed and acceleration are constrained to obtain the speed optimization curve. The follower vehicle uses a distributed receding horizon control method, which calculates the vehicle's speed optimization profile online. On the other hand, a linear following model is used to prevent collisions between vehicles and ensure the safety of the vehicle platoon. The simulation experiment has demonstrated that this speed optimization control method can reduce the fuel consumption of the vehicle platoon and ensure the safety of the vehicles.