In the process of formation flight, multiple UAVs have to meet the constraints of collision avoidance between the UAVs, communication distance, and obstacle avoidance. In order to realize trajectory tracking and formation keeping of a multi-UAV system on the premise of meeting the above constraints, a distributed model predictive control algorithm considering multiple constraints is designed. Firstly, the linear time-invariant motion models of the single UAV and formation system are established without considering the communication time delay, external interference and noise. Then, the distributed model predictive control algorithm is designed based on the virtual leader strategy, considering various constraints such as state constraints, input constraints, obstacle avoidance, collision avoidance and communication between individuals, with trajectory tracking and formation keeping as the control objectives. Furthermore, the feasibility of the optimization problem and the asymptotic stability of the formation system are analyzed, the keys to ensure the stability of the system are the designs of the terminal part and compatibility constraints of the algorithm. Finally, the effectiveness of the control algorithm is verified by the simulation of six UAVs.