Conventional magnetorheological dampers are usually powered continuously by coils, which not only increase energy consumption but also reduce the service life of a device. Based on the shearing principle of magnetorheological gel (MRG), a novel shearing magnetorheological gel damping device was designed in this paper. The permanent magnets and coils were used to jointly control the magnitude and direction of the device's magnetic field, and the damping force magnitude was controlled by changing the magnetization level of MRG. The device was installed at the bottom floor of a two-story steel frame-structure model, and the shaking table test of the magnetorheological damping structure was carried out using the constant current control method. The control effects of the damping system on different seismic waves under different currents were analyzed. Results show that the MRG damping device can significantly reduce the dynamic response of the structure; the damping effect varies for different seismic waves, and the damping effect decreases with increasing peak acceleration.