Aiming at the problems of nonlinearity and serious confusion of fault characteristics in analog circuits, this paper proposed a fault diagnosis method for an analog circuit based on ensemble empirical pattern decomposition (EEMD) and improved multifractal detrended fluctuations analysis (MF-DFA). This method consists of three steps: preprocessing, feature extraction, and fault classification identification. First, the EEMD decomposition preprocesses (denoises) the original signal; then, the appropriate IMF components are selected by correlation analysis; then, the IMF components are processed by the improved MF-DFA, and the fault feature values are extracted by calculating the multifractal spectrum parameters, and then the feature values are input to a support vector machine (SVM) for classification, which enables the diagnosis of soft faults in analog circuits. The experimental results show that the proposed EEMD-improved MF-DFA method effectively extracts the features of soft faults in nonlinear analog circuits and obtains a high diagnosis rate.