In an uncertain dynamic airspace, the future trajectories of noncooperative aircrafts (obstacles) are very uncertain. Multiple unmanned aircraft vehicles (UAVs) must avoid colliding into noncooperative obstacles and keep a safe distance between each other. This poses a huge challenge to the unmanned aircraft system traffic management (UTM). To cope with the challenge, this paper puts forward an automatic separation management method for a formation of multiple UAVs based on trajectory prediction in 3D dynamic airspace. Firstly, the uncertain trajectories of each obstacle in a time horizon were predicted based on the reachable set, producing an ellipsoidal reachable region. Next, a safe and efficient double-layer separation management strategy was proposed based on the improved artificial potential field (APF) method, considering the safe distance between cooperative UAVs and that between cooperative and noncooperative UAVs. The distance-based traditional APF method was adopted to manage the conflicts according to the reachable region of each obstacle, maximizing the safety between the UAV and the obstacle. The APF method based on relative motion state was employed to manage the conflicts, and adaptively adjust the dynamic safe separation between the UAVs. Experimental results prove that our method can effectively prevent the conflicts between a UAV and other UAVs in the formation or noncooperative obstacle. Besides, the collision-free trajectory generated by our method is smooth and stable, and close to the planned trajectory. The proposed method provides a solid guarantee to UAV flight safety, while minimizing the impacts on nearby aircrafts. The research findings shed new light on the UTM of highly uncertain low-altitude airspaces.