Due to changes in wind, the torque obtained from the wind turbine always fluctuates. Here, the wind turbine and the rotor of the generator are connected by a shaft that is one elastic body, and each rotating body has different inertia. The difference in inertia between the wind turbine and the generator causes a torsion between the wind generator and the generator; metal fatigue and torsion can damage the shaft. Therefore, it is necessary to consider the axial torsional vibration suppression of a geared wind power generator using a permanent magnet synchronous generator (PMSG). In addition, errors in axis system parameters occur due to long-term operation of the generator, and it is important to estimate for accurate control. In this paper, we propose torque estimation using H ∞ observer and axial torsional vibration suppression control in a three inertia system. The H ∞ controller is introduced into the armature current control system (q-axis current control system) of the wind power generator. Even if parameter errors and high-frequency disturbances are included, the shaft torsional torque is estimated by the H ∞ observer that can perform robust estimation. Moreover, by eliminating the resonance point of the shaft system, vibration suppression of the shaft torsional torque is achieved. The results by the proposed method can suppress axial torsional vibration and show the effect better than the results using Proportional-Integral (PI) control.