In this study, the dynamic range and dispersion stability of a shear-type magnetorheological (MR) grease damper were experimentally investigated as important characteristics affecting the performance of semi-active vibration suppression. Furthermore, the damper was applied to the semi-active vibration suppression of a small single-degree-of-freedom model structure subjected to seismic excitation. The performance test results of the damper indicated that it has a dynamic range of 157 times, which is much higher than that of conventional MR dampers. Also, because of the high dispersion stability of MR grease, the results showed that its performance can be kept for 9 days longer in comparison with a similar damper using MR fluid. Moreover, the structural vibration suppression test results demonstrated that the damper can suppress vibration response over a wide frequency range by applying skyhook-based control, which can take full advantage of the damper’s high dynamic range.