The spectral kurtosis analysis (KA) is used to select the filter parameters (FPs) combined with the application of the demodulation resonance technique (DRT) for a gearbox fault diagnosis (FD) of wind turbine. Based on the proposed method, the FPs can be selected automatically according to the kurtosis maximization principle. By changing of the shaft speed under the variable loads conditions, the natural frequency (NF) of the gearbox will be shifted and will affect the accuracy of the detection of the faults. So, the effect of the external loads on the NF of the gearbox is examined based on the simulation of the gearbox. In addition, the fast kurtogram (FK) combined with the demodulated resonance technology is used to process the simulated faulty signal of a gearbox. The results show that the FD of the gearbox is modified by correcting the NF shifts due to the variation of the operating loads.