With the modern air combat environment is becoming more and more complex, and the combat situation is changing rapidly, so it is important to explore a fast and effective decision-making method. In this paper, we propose an LSTM-MADDPG-based multi-aircraft collaborative beyond-visual-range air warfare decision algorithm to study the problem of multi-aircraft collaborative confrontation. Firstly, a beyond-visual-range air combat environment is established, including UAV movement model, radar detection zone model and missile attack zone model. Then, the multi-aircraft collaborative beyond-visual-range air warfare decision-making algorithm is proposed: a centralized training distributed execution architecture and the state space of the collaborative air warfare system are designed to deal with the synchronous decision-making problem among multiple UAVs; a learning rate decay mechanism is designed to improve the convergence speed and stability of the network; the network structure is improved using a long and short-term memory network to enhance the network's ability to extract tactical features; a decay-based factor-based reward function mechanism to enhance the cooperative countermeasure capability of UAVs. Finally, the results show that the proposed algorithm enables UAVs to have the ability of collaborative attack and defenses, while the algorithm has good stability and convergence.