With the emergence of Internet-of-Things (IoT) and big data technologies, data-driven fault diagnosis approaches, notably deep learning (DL)-based methods, have shown promising capabilities in achieving high accuracy through end-to-end learning. However, these deterministic neural networks cannot incorporate the prediction uncertainty, which is critical in practical applications with possible out-of-distribution (OOD) data. This present article develops a reliable and intelligent fault diagnosis (IFD) framework based on evidence theory and improved visual geometry group (VGG) neural networks, which can achieve accurate and reliable diagnosis results by incorporating additional estimation of the prediction uncertainty. Specifically, this article treats the predictions of the VGG as subjective opinions by placing a Dirichlet distribution on the category probabilities and collecting the evidence from data during the training process. A specific loss function assisted by evidence theory is adopted for the VGG to obtain improved uncertainty estimations. The proposed method, which incorporates evidential VGG (EVGG) neural networks, as termed here, is verified by a case study of the fault diagnosis of rolling bearings, in the presence of sensing noise and sensor failure. The experimental results illustrate that the proposed method can estimate the prediction uncertainty and avoid overconfidence in fault diagnosis with OOD data. Also, the developed approach is shown to perform robustly under various levels of noise, which indicates a high potential for use in practical applications.