This paper proposes a self-centering rocking dual-core braced frame system with buckling-restrained fuses (SC-RDC-BRF). While providing low-damage design and improved seismic resilience, the proposed system prevents soft-story failure in steel braced frames. The use of buckling-restrained fuses and post-tensioned (PT) cables in the SC-RDC-BRF system enables the structure to dissipate energy and exhibit self-centering behavior effectively. The proposed rocking system does not require column uplifting and thus preventing demand amplifications on the frame members. The paper also develops a design method for SC-RDC-BRF systems. The design method is based on a preliminary design with a rigid core assumption and a modified response spectrum analysis for the design of the rocking cores (i.e., beams, columns, braces, and ties). Nonlinear static and dynamic analyses are also performed on three-, six-, and nine-story frames to verify and illustrate the design method. Results from nonlinear response history analyses confirm the adequacy of the proposed design method and expected per-formance of SC-RDC-BRF systems.