Analog circuits need more effective fault diagnosis methods. In this study, the fault diagnosis method of analog circuits was studied. The fault feature vectors were extracted by a wavelet transform and then classified by a generalized regression neural network (GRNN). In order to improve the classification performance, a wolf pack algorithm (WPA) was used to optimize the GRNN, and a WPA-GRNN diagnosis algorithm was obtained. Then a simulation experiment was carried out taking a Sallen–Key bandpass filter as an example. It was found from the experimental results that the WPA could achieve the preset accuracy in the eighth iteration and had a good optimization effect. In the comparison between the GRNN, genetic algorithm (GA)-GRNN and WPA-GRNN, the WPA-GRNN had the highest diagnostic accuracy, and moreover it had high accuracy in diagnosing a single fault than multiple faults, short training time, smaller error, and an average accuracy rate of 91%. The experimental results prove the effectiveness of the WPA-GRNN in fault diagnosis of analog circuits, which can make some contributions to the further development of the fault diagnosis of analog circuits.