The purpose of this paper is to present a design method for friction damper (FD) for inelastic response control of short-period structure. A critical design parameter of FD is maximum friction force (MFF) and previous study evaluated MFF using equivalent damping ratio which is based on the maximum displacement. This procedure, however, gives the overestimated MFF for short-period structure. In this study, MFF of FD is evaluated based on RMS displacement response which is obtained by using given maximum response and peak factor. Numerical analysis shows that proposed method provide a reasonable MFF of FD for short-period structure.