The Self-centering Energy-absorbing Dual Rocking Core system (denoted as the SEDRC system) is a newly developed high-performance steel lateral force-resisting system that can achieve negligible residual inter-story drifts and avoid structural damage during rare earthquakes. Compared to many existing re-centering systems, the SEDRC system also has larger deformability and can obtain a more uniform inter-story drift responses when subjected to ground motions. This research focuses on developing a performance-based design procedure for the SEDRC systems. The seismic force reduction factor model and constant-ductility demand model have been derived via parametric nonlinear dynamic analyses of single-degree-of-freedom systems with the hysteretic behavior of the SEDRC system for developing the Displacement-Based Design (DBD) procedure. Following the developed DBD method, three six-story SEDRC systems with different parameters have been designed to achieve the desired performance objectives. Systematic numerical studies, including nonlinear static analyses, nonlinear dynamic analyses, and incremental dynamic analyses, have been conducted to validate whether the designed SEDRC system can obtain the prescribed performance target and investigate the effect of some design parameters on the seismic responses of the SEDRC systems. According to the results from the numerical studies, it can be observed that the three SEDRC systems designed through the proposed DBD method can successfully obtain the desired performance target. Moreover, higher inter-story drift at the bearing of the shear friction spring damper, as well as the higher enhanced yield-strength ratio of BRBs, can enhance the collapse-resistant capacity of the SEDRC system. Higher bearing inter-story drift can further reduce the residual inter-story drift leading to a lower collapse probability of the SEDRC system subjected to rare seismic events.