Multi-vehicle autonomous driving has attracted significant attention from academia and industries due to its ability to improve traffic efficiency and enhance the safety of drivers and passengers. In this paper, a distributed motion planning strategy based on the artificial potential field method is proposed to achieve overtaking of the autonomous vehicle fleet in dynamic environments. Firstly, a dynamic target tracking control protocol is constructed for an autonomous vehicle fleet using a modified artificial potential field. The target tracking control protocol overcomes the disadvantage of the traditional artificial potential field method (i.e., the dynamic target cannot be reached). Besides, a distributed obstacle avoidance control protocol is also designed to avoid potential collisions during the overtaking process. Finally, simulation experiments are performed to verify the feasibility and effectiveness of the proposed algorithm.