The wind turbine bearing is the core component to ensure the normal operation of a wind turbine. The noise pollution of the collected vibration signal is serious, the ordinary method is difficult to demodulate, and the operation is complex. In addition, with the increasing installed capacity of wind turbines, the signal samples based on the Shannon sampling theorem are also increasing, which brings great pressure to data transmission and storage. Deep learning based on big data-driven for wind turbine running condition monitoring plays an effective role in the field of fault diagnosis. However, the data training depends on a large amount of data and takes a long time. Therefore, a new method of wind turbine bearings fault diagnosis based on compressed sensing and Alexnet (CS-C-Alexnet) is proposed in this paper. Firstly, the signal is tracked by the stagewise orthogonal matching pursuit to find the sparsity coefficient of the signal, which facilitates the transmission and storage of the signal. Secondly, the signal is recovered by using the compressed sensing theory. This process can reduce the noise of the signal while recovering the signal. Next, any section of the normal running signal is selected as the approximate standard signal, the vibration data with fault and the standard signal are used to capture the fault data with the same phase by using the correlation coefficient. The captured signal is compared with the standard signal by subtraction to obtain the fault characteristic signal of this type. Then, the wavelet spectrum is obtained by continuous wavelet transform with the obtained characteristic signal. Finally, the wavelet spectrum is transferred to the trained Alexnet network for feature classification. The method was tested and the accuracy of fault diagnosis reached 99%, which proved that the method has a good fault diagnosis effect.