The current challenge in drone swarm technology is three-dimensional path planning and adaptive formation changes. The traditional A* algorithm has limitations, such as low efficiency, difficulty in handling obstacles, and numerous turning points, which make it unsuitable for complex three-dimensional environments. Additionally, the robustness of drone formations under the leader–follower mode is low, and effectively handling obstacles within the environment is challenging. To address these issues, this study proposes a virtual leader mode for drone formation flight and introduces a new Theta*–APF method for three-dimensional space drone swarm path planning. This algorithm optimizes the A* algorithm by transforming it into an omnidirectional forward Theta* algorithm. It also enhances the heuristic function by incorporating artificial potential field methods in a three-dimensional environment. Formation organization and control of UAVs is achieved using speed-control modes. Compared to the conventional A* algorithm, the Theta*–APF algorithm reduces the search time by about 60% and the trip length by 10%, in addition to the safer flight of the UAV formation, which is subject to artificial potential field repulsion by about 42%.