A new fault feature extraction method based on empirical mode decomposition (EMD) and composite multi-scale entropy (CMSE) is proposed, according to the characteristics of analog circuits, such as high integration, nonlinearity and easy to be affected by environment. Firstly, the output signal of the circuit is obtained by simulation. Secondly, the limited intrinsic mode components and a residual component are obtained by empirical mode decomposition. Then, the composite multi-scale entropy algorithm is used to calculate the sample entropy values of these limited intrinsic mode components in different time scales, and the feature vectors which can reflect the circuit fault are constructed. Finally, these fault feature vectors are input into BP neural network for training and testing, and the fault categories of the circuit are diagnosed. The results show that the method can effectively extract the fault characteristic parameters in the circuit, and has a high accuracy in identifying different types of circuit faults.