To analyze the multi-dimensional seismic mitigation performance and the torsional vibration characteristic of an L-shaped frame structure with a magnetorheological damper (MRD). Firstly, the mechanical property of the MRD is experimentally studied. Then, the calculation models of the L-shaped frame structure without and with MRDs are found through theoretical analysis, and the programs of the calculation models are compiled. Finally, the time history responses of the calculation models are calculated during the excitation of bi-directional seismic wave; the responses of displacement, acceleration, story drift ratio, shear force and bending moment and torsional vibration are then compared and analyzed. The results show that by adjusting the current, the damping force provided by the MRD can be adjusted continuously in the range of 3.1 to 120 kN. The compiled calculation model programs of the L-shaped frame structure without and with MRDs can effectively simulate the multi-dimensional seismic response of the structure. Reasonable arrangement of MR dampers can effectively reduce the displacement, acceleration, shear force, bending moment, multi-dimensional vibration, and torsional vibration response of L-shaped frame structures.