Detection and classification of breast lesions using mammographic images are one of the most difficult studies in medical image processing. A number of learning and non-learning methods have been proposed for detecting and classifying these lesions. However, the accuracy of the detection/classification still needs improvement. In this paper we propose a powerful classification method based on sparse learning to diagnose breast cancer in mammograms. For this purpose, a supervised discriminative dictionary learning approach is applied on dense scale invariant feature transform (DSIFT) features. A linear classifier is also simultaneously learned with the dictionary which can effectively classify the sparse representations. Our experimental results show the superior performance of our method compared to existing approaches.