Breast cancer is a leading cause of death in women worldwide, and early detection is crucial for successful treatment. Computer-aided diagnosis (CAD) systems have been developed to assist doctors in identifying breast cancer on ultrasound images. In this paper, we propose a novel fuzzy relative-position-coding (FRPC) Transformer to classify breast ultrasound (BUS) images for breast cancer diagnosis. The proposed FRPC Transformer utilizes the self-attention mechanism of Transformer networks combined with fuzzy relative-position-coding to capture global and local features of the BUS images. The performance of the proposed method is evaluated on one benchmark dataset and compared with those obtained by existing Transformer approaches using various metrics. The experimental outcomes distinctly establish the superiority of the proposed method in achieving elevated levels of accuracy, sensitivity, specificity, and F1 score (all at 90.52%), as well as a heightened area under the receiver operating characteristic (ROC) curve (0.91), surpassing those attained by the original Transformer model (at 89.54%, 89.54%, 89.54%, and 0.89, respectively). Overall, the proposed FRPC Transformer is a promising approach for breast cancer diagnosis. It has potential applications in clinical practice and can contribute to the early detection of breast cancer.