To diagnose the fault in the pitch actuator of wind turbines which causes the change in pitch angles, a fault diagnosis method is proposed in this study. The method combines the interval prediction algorithm with the recursive subspace identification based on the variable forgetting factor algorithm. First, the recursive subspace identification based on the variable forgetting factor algorithm is used to estimate the linear parameter-varying model of the wind turbine, which solves the model uncertainty. Second, considering the boundary problem described by model uncertainties, the interval prediction algorithm is introduced based on the basis of the identification results. Moreover, whether the fault occurs or not is determined by judging whether the pitch angle is in the range of the upper and lower bounds. Thus, the robustness of fault detection is improved. Finally, the proposed approach is validated by simulation experiments.