Breast cancer becomes a significant public health problem in the world. During the early detection of breast cancer, it is a very challenging task to classify accurately the benign–malignant patterns in digital mammograms. This study proposes a new fully automated computer-aided diagnosis (CAD) system for breast cancer diagnosis with high-accuracy and low-computational requirements. The expectation–maximisation algorithm is investigated to extract automatically the region of interests (ROIs) within mammograms. The standard shape, statistical, and textural features of ROIs are extracted and combined with multi-resolution and multi-orientation features derived from a new feature extraction technique based on wavelet-based contourlet transform. A hybrid feature selection approach based on combining the support vector machine recursive feature elimination with correlation bias reduction algorithm is proposed. Also, the authors investigate a new similarity-based learning algorithm, called Q, for benign–malignant classification. The proposed CAD system is applied to real clinical mammograms, and the experimental results demonstrate the superior performance of the proposed CAD system over other existing CAD systems in terms of accuracy 98.16%, sensitivity 98.63%, specificity 97.80%, and computational time 2.2 s. This reveals the effectiveness of the proposed CAD system in improving the accuracy of breast cancer diagnosis in real-time systems.