The finite-time containment control for multi-agent systems only enables the followers be in the leaders convex hull, which does not realize the consensus control of the followers.To solve the problem, a containment consensus control algorithm in the form of piecewise function with finite-time convergence is proposed.In addition, in view of the unknown velocity information, a velocity observer is designed to estimate the velocity information.Through Lyapunovs second theorem and homogeneous finite-time stability theorem, it is proved that the leaders can realize finite-time containment control of the followers and the followers can achieve finite-time consensus.Finally, the effectiveness of the control algorithm is proved by a large number of numerical simulations.