Deep learning (DL)-based intelligent fault diagnosis methods have greatly promoted the development of the field of fault diagnosis due to their powerful feature extraction ability for handling massive monitoring data. However, most of them still suffer from the following three limitations. First, many existing DL-based intelligent diagnosis methods cannot extract proper discriminative features from signals with strong noise. Second, the interactions or relationships between signals are ignored, while they mainly focus on extracting temporal features from the signal. Third, owing to their black-box nature, the learned features lack interpretability, which hinders their application in the industry. To tackle these issues, an explainable graph wavelet denoising network (GWDN) is proposed to achieve intelligent fault diagnosis under noisy working conditions in this article. In GWDN, the collected signals are first transformed into graph-structured data to consider the interactions among signals. Then, the graph wavelet denoising convolution (GWDConv) is proposed based on the discrete graph wavelet frame, which allows GWDN to achieve multiscale feature extraction for graph-structured data and realize signal denoising. Extensive experiments are implemented to verify the efficacy of the proposed GWDN, and the experimental results show that GWDN can achieve state-of-the-art performance among the comparison methods. Besides, by using the square envelope spectrum to analyze the extracted features of GWDConv, we find that it can well retain the fault-related components of the signal and realize signal denoising, which further proves that GWDN is explainable.