Aiming at the multiple unmanned aerial vehicles (UAVs) trajectories planning problem, to expedite the convergence speed of the planning algorithm, a modified trust region-based sequence convex optimization (SCP) algorithm is proposed. Firstly, a non-convex optimization problem is constructed for multi-UAVs cooperative task. Then, by transforming non-convex constraints to convex constraints through discretization, linearization methods, etc., a convex optimization problem is formed. Secondly, the signed distance is introduced to represent the non-convex constraint of obstacle avoidance. The constraint between discrete points is introduced to ensure the flight safety of UAVs in continuous time. Finally, a fast trajectory planning method for multi-UAVs based on SCP with modified trust region is designed, and the effectiveness of the proposed algorithm is verified by experiments.