A design method of adaptive fuzzy damping controller for stay cable-magnetorheological system with supervision function was proposed on fuzzy estimation and observation theory，which took the vibration reduction of stay cables as the application object to solve the practical engineering problems in magnetorheological damping control, such as difficult to determine boundary conditions, unknown external excitation, modeling and structural errors in the system. In the controller design, the fuzzy estimation and adaptive compensator strategies were used to reduce the influence of unknown excitation mutation, parameters and modeling estimation errors on the damping control performance, and the supervisory control method was introduced to supervise the vibration reduction control performance. The control accuracy of the damping control system was improved. Based on the Lyapunov method, it was proved that the state of the stay cable-magnetorheological damper system was bounded and asymptotically stable, and the stay cable converged with small vibration velocity and small amplitude. Finally, the simulation verification was carried out by taking the stay cable C20 of Ningbo Zhaobaoshan cable-stayed bridge as an example, and the simulation results showed that the method was robust to unknown external excitation disturbance and uncertain system structure, and the damping effect was outstanding.