The controllable containment control for second-order directed multi-agent networks under given topologies is investigated. For the problem that the controllable configuration issues have not been considered between leaders and followers for most of the results of containment control, the complex network controllability theory and the maximum bipartite graph matching algorithm are combined to determine the leader and follower set meeting the network controllable. By using the designed corresponding control protocol for followers, all followers are driven to converge to the stationary convex hull with the leaders in order to achieve the controllability containment control of the networks. Simulation results show the correctness of the theoretical analysis.