Recent developments in multiagent consensus problems have heightened the role of network topology when the agent number increases largely. The existing works assume that the convergence evolution typically proceeds over a peer-to-peer architecture where agents are treated equally and communicate directly with perceived one-hop neighbors, thus resulting in slower convergence speed. In this article, we first extract the backbone network topology to provide a hierarchical organization over the original multiagent system (MAS). Second, we introduce a geometric convergence method based on the constraint set (CS) under periodically extracted switching-backbone topologies. Finally, we derive a fully decentralized framework named hierarchical switching-backbone MAS (HSBMAS) that is designed to conduct agents converge to a common stable equilibrium. Provable connectivity and convergence guarantees of the framework are provided when the initial topology is connected. Extensive simulation results on different-type and varying-density topologies have shown the superiority of the proposed framework.