The mechanical fault of gas-insulated switchgear (GIS) seriously threatens the security of the power grid. Recently, acoustic-based fault diagnosis methods, which have the advantage of non-contact measurement, have been applied to the GIS mechanical fault diagnosis, but vulnerable to the interference of the background noise. To improve the capacity of the acoustic-based GIS fault diagnosis under noise background, by simulating the sound feature extraction ability and anti-noise ability of human auditory system, a novel GIS mechanical fault diagnosis method based on saliency feature of auditory brainstem response (SFABR) is proposed. First, an auditory saliency model, which considers both the auditory periphery and the auditory nerve center was constructed by combining the deep auditory model and the saliency model. After processing GIS emitted acoustic signal, the auditory brainstem response (ABR) was obtained, and the saliency features of the ABR were extracted to obtain the SFABR. Then, the characteristic frequency distribution of the auditory saliency model was adjusted to make it more suitable for the spectral characteristics of the GIS sound signal. Finally, the SFABR was mapped to a two-dimensional CNN to train a model for GIS mechanical fault diagnosis. This method simulates the process of auditory response extraction and the selection effect of auditory attention on sound elements. The 110 kV three-phase GIS fault simulation experiment shows that for GIS mechanical faults, the diagnosis method based on SFABR can obtain 96.1% fault identification accuracy. In different noise environments, compared with the traditional acoustic-based fault diagnosis methods, this method has stronger anti-noise performance, and can more effectively realize the identification of GIS mechanical failure types. In future research, the method can be further extended to fault diagnosis of more types of power equipment.