The kinematic constraints of underwater robotic fish and the leader selection in containment control are considered in this paper. Combining the controllability theory with containment control, for the directed multiple robotic fish system, a controllable containment control algorithm of multiple robotic fish based on bipartite graph maximum matching is proposed. Firstly, aiming at the directed network topology of multiple robotic fish, the maximum matching algorithm of bipartite graph is used to get the driving nodes satisfying the system controllable as leaders, the others are followers. Then, the corresponding containment control protocol is designed for the model of 2D simulation robotic fish. Thus, the controllable containment control of multiple robotic fish system is achieved and the rigid body long side direction of follower fish is consistent with leaders. The Lyapunov stability theory is used to prove the stability of the system. Finally, two groups of simulation experimet on the URWPGSim2D multiple robotic fish simulation platform are carried out. One group randomly selects leaders, and the other group uses the bipartite maximum matching algorithm to determine the leaders. Simulation results show that the proposed algorithm can effectively realize the controllable containment control of multiple robotic fish.