The study of the vibration reduction characteristics of SFD to the bending-torsional coupled vibration of the dual-rotor system can provide support for the structural design of aero-engines. Based on the overall eccentric disc model, the bending-torsional coupling dynamic equation of the dual-rotor system is established in this paper. The amplitude and nonlinear periodic characteristics of the dual-rotor system are obtained by combining Newmark-β method and Newton-Raphson method. The results show that the vibration reduction effect of SFD on bending-torsional coupling vibration is closely related to the speed. The vibration reduction effect of SFD is weak at the first-order critical speed range and below, and reduces the torsional amplitude by 70 % at the second-order critical speed range and above. SFD kept the bending-torsional coupling vibration of the dual-rotor system stable in a stable 5-period motion state.