The lateral stiffness of the external frame and internal core tube (CT) in super‐tall CT structures exhibits significant differences. This paper presents a novel centralized damping structural system (CDS), which utilizes the differential lateral displacements of the internal and external substructures by centrally installing centralized damping devices between the CT and the external frame to achieve energy dissipation and seismic mitigation objectives. First, a theoretical analysis model for CDS was established, and its dynamic transfer function was derived. Parameter analysis was conducted to investigate the influencing factors. The optimal damping ratio for CDS is determined using the fixed‐point theory. Experimental shake table tests were performed to validate the seismic mitigation effectiveness of CDS, of which the results demonstrate significant reductions in both the top‐level acceleration of the internal frame and the top‐level displacement of the external frame. Finally, comparative numerical analyses are performed between traditional structures and the CDS structures, revealing that the centralized damping structral system can effectively reduce the acceleration of the internal CT and the interstory displacement of the external frame. The CDS structure achieves superior seismic mitigation effects compared to traditional structures with fewer damping devices.