Bearings are important part of aerospace equipments. Therefore, bearings fault diagnosis and fault detection is necessary for the safe operation. Generally, the bearing are core component and runs in a complex and heavy background noise environment. Thence, the bearing signals will be overwhelmed by noise. At present, the diagnosis methods of bearings are based on the experience of experts which costs a lot of labor and time-consuming. Consequently, to address these inadequacies, a novel method based on variational mode decomposition (VMD) algorithms and Alexnet neural network has been presented. Firstly, it decomposes the nonstationary bearing signals into intrinsic mode functions adaptively. However, background noise will seriously affect the number of signal decompositions and reduce accuracy even over-decomposition. Thence, this paper proposed the hierarchical fuzzy entropy method to adaptively extract weak fault characteristics of bearings. Then Alexnet neural network has been utilized to learn the relationship of fault features and bearings health conditions. The architecture of Alexnet diagnosis model is convenient and efficient. Finally, two tentative dataset are adopted to verify the effectiveness and feasibility of the method proposed in this article. The results show that the presented method has a higher fault diagnosis accuracy rate than traditional convolutional neural networks.