This study proposes a dual-coil magnetorheological torsional vibration damper (MRTVD) and verifies the effectiveness of semi-active damping control to suppress the shaft system’s torsional vibration via experimental research. Firstly, the mechanical model of the designed MRTVD and its coupling mechanical model with the rotating shaft system are established. Secondly, the torsional response of the shaft system is obtained via resonance experiments, and the influence of the current on the torsional characteristics of the magnetorheological torsional damper is analyzed. Finally, the MRTVD is controlled using the skyhook control approach. The experimental results demonstrate that when the main shaft passes through the critical speed range at various accelerations, the amplitude of the shaft’s torsional vibration decreases by more than 15%, and the amplitude of the shaft’s torsional angular acceleration decreases by more than 22%. These conclusions validate the inhibitory effect of MRTVD on the main shaft’s torsional vibrations under skyhook control.