In this paper, a computer aided breast cancer diagnosis system using Non sub sampled Shearlet Transform (NSST) is proposed. A two-step approach is developed to classify the given mammogram. At first, the given mammogram is classified into abnormal or normal followed by the classification of abnormal severity into either malignant or benign using support vector machine classifier. The proposed approach uses shearlet moments to classify the digital mammograms. From the shearlet coefficients, up to 4th order moments are computed. The results shows that the method based on shearlet moments is very robust over other multiresolutional analysis such as wavelet and curvelet transform. Also, it presents an excellent classification rate of over 90% for all considered cases.