Reinforcement learning (RL)–based car-following (CF) control strategies have attracted significant attention in academia, emerging as a prominent research topic in recent years. Most of these control strategies focus solely on the motion status of the immediately preceding vehicle. However, with the development of vehicle-to-vehicle (V2V) communication technologies, intelligent vehicles such as connected autonomous vehicles (CAVs) can gather information about surrounding vehicles. Therefore, this study proposes an RL-based CF control strategy that takes multivehicle scenarios into account. First, the trajectories of two preceding vehicles and one following vehicle relative to the subject vehicle (SV) are extracted from a highD dataset to construct the environment. Then the twin-delayed deep deterministic policy gradient (TD3) algorithm is implemented as the control strategy for the agent. Furthermore, a sequence-to-sequence (seq2seq) module is developed to predict the uncertain motion statuses of surrounding vehicles. Once integrated into the RL framework, this module enables the agent to account for dynamic changes in the traffic environment, enhancing its robustness. Finally, the performance of the CF control strategy is validated both in the highD dataset and in two traffic perturbation scenarios. In the highD dataset, the TD3-based prediction CF control strategy outperforms standard RL algorithms in terms of convergence speed and rewards. Its performance also surpasses that of human drivers in safety, efficiency, comfort, and fuel consumption. In traffic perturbation scenarios, the performance of the proposed CF control strategy is compared with the model predictive controller (MPC). The results show that the TD3-based prediction CF control strategy effectively mitigates undesired traffic waves caused by the perturbations from the head vehicle. Simultaneously, it maintains the desired traffic state and consistently ensures a stable and efficient traffic flow.