In turbulent wind excitation scenarios, the shaft system drive chain of the doubly-fed wind power generation system exhibits wideband forced torsional vibration in the low-frequency range, which affects the stable operation of the turbine. A Model Reference Adaptive Control (MRAC) method for torsional vibration suppression is proposed. A wideband forced torsional vibration model of the shaft system considering optimal torque control and bandpass filter parameters is established. The feedforward controller and adaptive control law are designed based on the system input and output to address the challenge of difficult measurement of transmission chain state variables. The adaptive adjustment of the main parameters of the bandpass filter with active damping provided to the transmission chain of the doubly-fed wind power generation system allows the dynamic response of the transmission chain to track the stable reference model. Taking a 1.5MW doubly-fed wind power generation system as an example, the tracking effect of MRAC is simulated and verified under sustained turbulent wind excitation scenarios. The suppression effect of wideband forced torsional vibration is compared between the electrical damping reshaping method and the MRAC method. The results show that the proposed MRAC method can achieve stable tracking of the controlled object with a tracking average error not exceeding 4.94%. Compared to the electrical damping reshaping method, adopting MRAC in the doubly-fed wind power generation system improves the suppression effect of wideband forced torsional vibration by 21.77%. The fluctuations in flexible transmission shaft torque and generator active power output are both reduced.