To address failures of wind turbine pitch-angle sensors, traditional wind turbine linear parameter varying (LPV) model is transformed into a double-layer convex polyhedron LPV model. On the basis of this model, when the plurality of the sensor undergoes failure and details of the failure are inconvenient to obtain, each sub-controller is designed using distributed thought and gain scheduling method. The final controller is obtained using all of the sub-controllers by a convex combination. The design method corrects the errors of the linear model, improves the linear degree of the system, and solves the problem of multiple pitch angle faults to ensure stable operation of the wind turbine.