A combination of spectral kurtosis (SK), based on Choi–Williams distribution (CWD) and hidden Markov models (HMM), accurately identifies initial gearbox failures and diagnoses fault types of gearboxes. First, using the LMD algorithm, five types of gearbox vibration signals are collected and decomposed into several product function (PF) components and the multicomponent signals are decomposed into single-component signals. Then, the kurtosis value of each component is calculated, and the component with the largest kurtosis value is selected for the CWD-SK analysis. According to the calculated CWD-SK value, the characteristics of the initial failure of the gearbox are extracted. This method not only avoids the difficulty of selecting the window function, but also provides original eigenvalues for fault feature classification. In the end, from the CWD-SK characteristic parameters at each characteristic frequency, the characteristic sequence based on CWD-SK is obtained with HMM training and diagnosis. The experimental results show that this method can effectively identify the initial fault characteristics of the gearbox, and also accurately classify the fault characteristics of different degrees.