In this study, a simplified design procedure for friction dampers of a multi-story structure in order to reduce seismic response is proposed. To get insight for control effect of the structure with friction dampers is difficult, because of a nonlinear characteristic by a friction damper. Since a control force of a friction damper is influenced by coupling velocity between floors, adjoining modes are coupled. Thus structural response are derived by assuming steady-state response in resonance. As it is impossible that an exact solution is obtained for seismic load, first, a closed form solution can be achieved under harmonic vibration. Second, to convert a three-story building into a single-degree-of-freedom(SDOF) structure, modal analysis is performed. Third, an equivalent damping ratio is derived with utilizing closed form solution. And response reducing factor is proposed by it. Finally, friction force of a damper is designed for using response reducing factor, and then designed dampers are verified for seven seismic data. The nonlinear analysis results confirm the validity of the proposed procedure.