Under turbulent wind excitation, the drive chain of the shaft system in doubly-fed wind power generation systems experiences wideband forced torsional vibrations in the low-frequency range, compromising the stable operation of the turbine. To address this issue, a model reference adaptive control (MRAC) method for torsional vibration suppression is proposed. A wideband forced torsional vibration model is established, incorporating optimal torque control and bandpass filter parameters. To overcome the challenge of unmeasurable transmission chain state variables, a feedforward controller and an adaptive control law are designed based on system inputs and outputs. The bandpass filter parameters are adaptively adjusted to provide active damping, enabling the transmission chain’s dynamic response to track a stable reference model. Using a 1.5 MW doubly-fed wind power generation system as a case study, the effectiveness of MRAC is validated through simulations under sustained turbulent wind conditions. The torsional vibration suppression performance of the MRAC method is compared with that of the electrical damping reshaping method. Results show that the proposed MRAC method achieves stable tracking of the controlled object, with an average tracking error not exceeding 4.94%. Compared to the electrical damping reshaping method, MRAC improves wideband torsional vibration suppression by 21.77%, and significantly reduces fluctuations in both shaft torque and generator active power output.