The development of connected and automated vehicles (CAV) technology not only helps to reduce traffic accidents and improve traffic efficiency, but also has significant potential for energy saving and emission reduction. Using the dynamic traffic flow information around the vehicle to optimize the vehicle trajectory is conducive to improving the energy efficiency of the vehicle. Therefore, an energy-efficient driving method for CAVs based on reinforcement learning is proposed in this paper. Firstly, a set of vehicle trajectory prediction models based on long and short-term memory (LSTM) neural networks are developed, which integrate driving intention prediction and lane change time prediction to improve the prediction accuracy of surrounding vehicle trajectories. Secondly, an energy-efficient driving model is built based on Proximity Policy Optimization (PPO) reinforcement learning. The model takes the current states and predicted trajectories of surrounding vehicles as input information, and outputs energy-saving control variables while taking into account various constraints, such as safety, comfort, and travel efficiency. Finally, the method is tested by simulation on the NGSIM dataset, and the results show that the proposed method can save energy consumption by 9–22%.