Seismic control performance of the magnetorheological (MR) damper, which has strong nonlinearity, varies with the dynamic characteristics of the structure and ground motion such as natural period, peak ground acceleration. The MR damper has a properly of the friction damper so that the relative magnitude of the friction force over excitation intensity affects the control performance. In this study, through numerical analyses of single-degree-of-freedom (SDOF) structures, design spectra for the passive MR damper and optimal non-dimensional friction forces are suggested. Additionally, simple semi-active control algorithms modulating the friction force of the MR damper in accordance with structural responses are proposed and compared with each other and the passive MR damper. Finally, the condition that the semi-active control is more appropriate than the passive one is identified for reasonable selection of the control strategy.