In this study, a seismic design methodology for a friction damper based on the story shear force of an elastic building structure is proposed. First, using two normalization methods for the slip-load of a friction damper, numerical analyses of various single-degree-of-freedom systems are performed. From those analyses, the effect of the slip-load and brace stiffness was investigated and the optimal stiffness ratio of the brace versus original structure was found. Second, from the numerical analysis for five multi-story building structures with different natural frequency and the number of story, reasonable decision method for the total number of installation floor, location of installation and distribution of slip-loads are drawn. In addition, an empirical equation on the optimal number of installation floor is proposed. Finally, the superiority of the proposed method compared to the existing design method is verified from the numerical analysis.