Abstract: This paper focuses on the mean square consensus problem of multi-agent system which has the nonconvex input and Markov switching graphs. First, a non-convex constraint operator is introduced and a distributed control algorithm is designed according to the neighbor node information in the multi-agent system. Then, based on the property of non-negative matrix, the sufficient and necessary conditions are obtained for the mean square consensus problem of the multi-agent system with Markov switching graphs. Finally, numerical simulation results validate that the mean square consensus can be achieved when the control input is restricted in a nonconvex set.