To solve the problem of formation containment control of multi-UAV system with several leaders under joint connected topology, distributed consensus controllers for leaders and followers are designed respectively.The Laplacian matrix is partitioned according to the leaders and followers.The Laplacian matrix with the directed spanning tree is decomposed, and the problem of formation control of the leader is simplified to the problem of asymptotic stability of the low-order time-varying system.The amount of control error is defined in the follower implementation, and the problem of containment control of the follower is simplified to the problem of asymptotic stability of the time-varying system.The averaging method is used, and the asymptotic stability of the two time-varying systems is transformed into that of two time-averaged systems.The design steps of the controller are given by using Linear Matrix Inequality (LMI) and Lyapunov function.The communication topology switching of the multi-UAV system is fast enough for the system to realize formation containment control under the condition of joint connected topology.The simulation results prove the effectiveness of the designed controller.