With the increasing of collision accidents among Unmanned Aerial Vehicles (UAVs) the collision avoidance has become a critical problem in free flight airspace of multi-UAV.Firstly a multi-UAV cooperative collision avoidance system was designed and then a novel model predictive control method(MPC) was presented.In the method Extended Kalman Filter (EKF) was used to predict trajectories of obstacles and target in uncertain environment the environment information was shared among UAVs by inter-UAV communication and multi-UAV cooperative collision avoidance guidance strategies were made based on MPC.The simulation results demonstrate the validity of the method and the obvious effect of cooperation mechanism.