To address the obstacle avoidance problem in multi-agent systems, this study proposes a reinforcement learning-based approach for multi-agent collaborative obstacle avoidance. First, a mathematical model for multi-agent obstacle avoidance is established, defining optimization objectives and constraints. Second, a joint state-action space is designed, and an optimal reciprocal collision avoidance (ORCA) algorithm is incorporated to construct the reward function, balancing avoidance efficiency and safety. Finally, simulation experiments compare the proposed method with the velocity obstacle (VO) method and ORCA. The results demonstrate that the proposed method outperforms traditional velocity obstacle and ORCA approaches in terms of path length, runtime, and motion smoothness. Moreover, it maintains algorithmic stability and generalization capability even as the number of agents increases.