Focusing on the multi-UAV formation collision avoidance problem, a prescribed-time distributed control method based on scaling potential function is proposed. Firstly, a non-jump time-varying function is designed to improve the prescribed-time stability criterion, which achieves fast and smooth convergence of systems. Secondly, a prescribed-time distributed observer is designed to compensate the composite disturbance without relying on the system disturbance and its derivatives. Thirdly, based on the above observer, the leading UAV's obstacle avoidance control strategy is further constructed by designing the scaling potential function, and a follower UAV collision avoidance control method is proposed based on the error transformation function, so that the UAVs can maintain the original formation while avoiding obstacles. Finally, the feasibility of the proposed method is proved by theoretical analysis and numerical simulation.