As the modern air combat environment grows increasingly complex and dynamic， the need for rapid and effective decision-making methods has become urgent. This paper proposes a multi-aircraft cooperative beyond-visual-range air combat decision-making algorithm based on long and short-term memory （LSTM） and multi-agent deep deterministic policy gradient （MADDPG） to address the challenge of collaborative confrontation of multiple unmanned aerial vehicles （UAVs）. First， a beyond-visual-range air combat environment is established， including the UAV movement model， the radar detection zone model， and the missile attack zone model. Second， the multi-aircraft collaborative beyond-visual-range air combat decision-making algorithm is proposed. This algorithm includes a centralized-training distributed-execution framework and a state space of the collaborative air combat system to handle synchronous decision-making across multiple UAVs， a learning rate decay mechanism to enhance network convergence speed and stability， an improved network based on LSTM to strengthen tactical feature extraction， and a decay-factor-based reward function to improve cooperative confrontation performance. Experimental results demonstrate that the proposed algorithm equips UAVs with effective collaborative attacking and defensive capabilities， while exhibiting strong stability and convergence.