Feature extraction methods and classifier selection are two critical steps in heart sound classification. To capture the pathological features of heart sound signals, this paper introduces a feature extraction method that combines mel-frequency cepstral coefficients (MFCC) and power spectral density (PSD). Unlike conventional classifiers, the adaptive neuro-fuzzy inference system (ANFIS) was chosen as the classifier for this study. In terms of experimental design, we compared different PSDs across various time intervals and frequency ranges, selecting the characteristics with the most effective classification outcomes. We compared four statistical properties, including mean PSD, standard deviation PSD, variance PSD, and median PSD. Through experimental comparisons, we found that combining the features of median PSD and MFCC with heart sound systolic period of 100–300 Hz yielded the best results. The accuracy, precision, sensitivity, specificity, and F1 score were determined to be 96.50%, 99.27%, 93.35%, 99.60%, and 96.35%, respectively. These results demonstrate the algorithm’s significant potential for aiding in the diagnosis of congenital heart disease.