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This study proposes the optimum design of chevron braced friction dampers (CBFDs) for the vulnerability control of steel moment–resisting frames (SMRFs) under mainshock-aftershock (MS-AS) sequences. First, the optimum parameters of the CBFD systems installed in the stories of an inelastic SMRF are found through minimizing the maximum damage index of stories averaged over seven scaled earthquake excitations. The uniform distribution of the story damage along the height of the controlled SMRF is adopted as constraint in the optimization procedure. The damage index is calculated based on the Park-Ang damage model which is expressed based on a linear combination of deformation, moment, and absorbed hysteretic energy of structural elements imposed by an earthquake excitation. Results reveal that the optimized CBFDs-equipped SMRF exhibits better distribution of the story damage than that of the uncontrolled SMRF. Finally, the vulnerability assessment of the optimized CBFDs-equipped SMRF under MS and MS-AS ground motions is investigated by the fragility curves. The fragility assessment emphasize that the optimized CBFDs effectively mitigate the seismic vulnerability of the controlled SMRF under MS-AS sequences at different damage states. • The optimum design of CBFDs was proposed for the vulnerability control of SMRFs under MS-AS sequences. • The maximum of the damage index of stories was considered as the objective function. • The objective function was averaged over seven scaled earthquake excitations. • The uniform distribution of the damage along the height of SMRF was defined as a constraint. • The CBFDs-equipped SMRF enhances structural/overall system performance under MS-AS sequences in all damage states. [ABSTRACT FROM AUTHOR]