Abstract: Under a connected bipartite graph topology, we investigate the group consensus problem of multi-agent systems for second-order continuous-time systems. Based on the properties of the connected bipartite graph, we design a group consensus control protocol based on competition for the second-order multi-agent systems. We analyze the group consensus and obtain the sufficient conditions for group consensus of the second-order multi-agent systems based on the algebraic graph and matrix theories. We then obtain the consensus equilibriums of the subgroups. The simulation results indicate that second-order multi-agent systems can achieve group consensus under a connected bipartite graph.