Seismic design of braced frames that simultaneously considers economic issues and structural performance represents a rather complicated engineering problem, and therefore, a systematic and well-established methodology is needed. This study proposes a multi-objective seismic design method for an inverted V-braced frame with suspended zipper struts that uses the non-dominated sorting genetic algorithm-II(NSGA-II). The structural weight and the maximum inter-story drift ratio as the objective functions are simultaneously minimized to optimize the cost and seismic performance of the structure. To investigate which of strength- and performance-based design criteria for braced frames is the critical design condition, the constraint conditions on the two design methods are simultaneously considered (i.e. the constraint conditions based on the strength and plastic deformation of members). The linear static analysis method and the nonlinear static analysis method are adopted to check the strength- and plastic deformation-based design constraints, respectively. The proposed optimal method are applied to three- and six-story steel frame examples, and the solutions improved for the considered objective functions were found.