This study combined a Convolutional Neural Network (CNN) with the chaos theory and the Empirical Mode Decomposition (EMD) method for the attenuation fault recognition of power capacitors. First, it built six capacitor analysis models, including normal capacitors, failed capacitors, and normal capacitors attenuated by 20-80%. Then a power testing machine was used for an applied voltage test of the capacitor. The EMD method was combined with the chaos synchronisation detection method to chart the discharge signals of the voltage and current that was captured by a high frequency oscilloscope into a 3D chaotic error scatter plot, as the fault diagnosis feature image. Finally, the CNN algorithm was used for the capacitor fault detection. The advantages of the proposed method are that big data are compressed to extract meaningful feature images, the operating state of the power capacitor can be detected effectively, and faults can be diagnosed according to the electrical signal change of the power capacitor. The actual measurement results showed that the accuracy of the proposed method was as high as 97% and has a high efficiency of noise rejection ability, which indicates that the method could be applied to other power-related fields in the future.