To address the issues in the cooperative path planning of UAV swarm in complex environments, where the traditional RRT algorithm exhibits poor path quality and the RRT* algorithm suffers from low planning efficiency and high path redundancy, this paper proposes an improved RRT* algorithm and applies it to the research on cooperative path planning of UAV swarm. Centering on the core performance of the algorithm, the following measures are adopted: a dynamic sampling strategy is employed to dynamically adjust the sampling probability based on obstacle distribution and the direction of the target point, thereby enhancing sampling pertinence; an adaptive step size adjustment is designed to adjust the step size in real time according to the current node and environment complexity; an enhanced reconnection mechanism is constructed to expand the search range of parent nodes for optimizing path cost; and a greedy algorithm pruning strategy is introduced to eliminate redundant path nodes so as to shorten the path length. On this basis, the improved RRT* algorithm is applied to the cooperative path planning of UAV swarm, and a cooperative path planning strategy integrating path collision and path time cooperation models is proposed. Additionally, a quadratic programming optimization strategy is combined to smooth and optimize the paths, further enhancing the global optimality and cooperativity of the swarm during flight. The results of simulation experiments show that the improved RRT* algorithm has significant advantages in path planning performance and can effectively meet the requirement of cooperative path planning for UAV swarm in complex environments.