In this paper, we aim to apply deep learning convolution neural network (Deep-CNN) technology to classify breast masses in mammograms. We develop a Deep-CNN combined with multi-feature extraction and transfer learning to detect breast cancer. The Deep-CNN is utilized to extract features from mammograms. A support vector machine (SVM) is then trained on the Deep-CNN features to classify normal, benign, and cancer cases. The scoring features from the Deep-CNN are coupled with texture features and used as inputs to the final classifier. Two texture features are included: texture features of spatial dependency and gradient-based histograms. Both are employed to locate breast masses in mammograms. Next we apply transfer learning to the classifier of the SVM. Four techniques are devised for the experimental evaluation of the proposed system. The fourth technique combines the Deep-CNN with texture features and local features extracted by the scale-invariant feature transform (SIFT) algorithm. Experiments are designed to measure the performance of the various techniques. The results demonstrate that the proposed CNN coupled with the texture features and the SIFT outperforms the other models and performs best with transfer learning embedded. The accuracy of this model is 97.8%, with a true positive rate of 98.45% and a true negative rate of 96%.