Globally, the incidence rate for breast cancer ranks first. Treatment for early-stage breast cancer is highly cost effective. Five-year survival rate for stage 0–2 breast cancer exceeds 90%. Screening mammography has been acknowledged as the most reliable way to diagnose breast cancer at an early stage. Taiwan government has been urging women without any symptoms, aged between 45 and 69, to have a screening mammogram bi-yearly. This brings about a large workload for radiologists. In light of this, this paper presents a deep neural network (DNN)-based model as an efficient and reliable tool to assist radiologists with mammographic interpretation. For the first time in the literature, mammograms are completely classified into BI-RADS categories 0, 1, 2, 3, 4A, 4B, 4C and 5. The proposed model was trained using block-based images segmented from a mammogram dataset of our own. A block-based image was applied to the model as an input, and a BI-RADS category was predicted as an output. At the end of this paper, the outperformance of this work is demonstrated by an overall accuracy of 94.22%, an average sensitivity of 95.31%, an average specificity of 99.15% and an area under curve (AUC) of 0.9723. When applied to breast cancer screening for Asian women who are more likely to have dense breasts, this model is expected to give a higher accuracy than others in the literature, since it was trained using mammograms taken from Taiwanese women.