Defect inspection, also known as defect detection, is significant in mobile screen quality control. There are some challenging issues brought by the characteristics of screen defects, including the following: (1) the problem of interclass similarity and intraclass variation, (2) the difficulty in distinguishing low contrast, tiny-sized, or incomplete defects, and (3) the modeling of category dependencies for multi-label images. To solve these problems, a graph reasoning module, stacked on a classification module, is proposed to expand the feature dimension and improve low-quality image features by exploiting category-wise dependency, image-wise relations, and interactions between them. To further improve the classification performance, the classifier of the classification module is redesigned as a cosine similarity function. With the help of contrastive learning, the classification module can better initialize the category-wise graph of the reasoning module. Experiments on the mobile screen defect dataset show that our two-stage network achieves the following best performances: 97.7% accuracy and 97.3% -measure. This proves that the proposed approach is effective in industrial applications.