According to the Health Promotion Administration in the Ministry of Health and Welfare statistics in Taiwan, over ten thousand women have breast cancer every year. Mammography is widely used to detect breast cancer. However, it is limited by the operator's technique, the cooperation of the subjects, and the subjective interpretation by the physician. It results in inconsistent identification. Therefore, this study explores the use of a deep neural network algorithm for the classification of mammography images. In the experimental design, a retrospective study was used to collect imaging data from actual clinical cases. The mammography images were collected and classified according to the breast image reporting and data-analyzing system (BI-RADS). In terms of model building, a fully convolutional dense connection network (FC-DCN) is used for the network backbone. All the images were obtained through image preprocessing, a data augmentation method, and transfer learning technology to build a mammography image classification model. The research results show the model's accuracy, sensitivity, and specificity were 86.37%, 100%, and 72.73%, respectively. Based on the FC-DCN model framework, it can effectively reduce the number of training parameters and successfully obtain a reasonable image classification model for mammography.