With the rapid development of low earth orbit (LEO) satellites, the ultra-dense LEO satellite-terrestrial integrated networking has become a promising paradigm to provide wide coverage, high capacity and flexible services for the sixth generation (6G) mobile communication networks. However, the natural heterogeneity, high dynamics, and large scale of ultra-dense LEO satellite networks pose new challenges to network control and management. To this end, in this article, we propose a medium earth orbit (MEO), low earth orbit (LEO) and satellite Earth stations (SESs) integrated multi-layered management architecture for the ultra-dense LEO satellite network, where global controllers and local controllers are introduced to reduce the network management complexity. With the aid of this hybrid multi-layered management framework, we can efficiently implement the network status control, mobility management, resource management, and service management in the satellite-terrestrial integrated network. To obtain proper global and local controllers with high management efficiency in the hybrid multi-layered network management architecture, we further propose a novel and efficient grouping and clustering method for the ultra-dense LEO satellite network, where each group manager MEO satellite and cluster head (CH) LEO satellites are respectively considered as the global and local controllers of each LEO satellite group. Numerical simulations are carried out to evaluate the superiority and effectiveness of the proposed hybrid multi-layered ultradense LEO networking management architecture.