A deep learning method using the fully-convolutional residual neural network (FCR-NN) was applied to segment the whole breast and fibroglandular tissue in 289 patients. The Dice similarity coefficient (DSC) value and accuracy were calculated as evaluation metrics. For breast segmentation, the mean DSC was 0.85 with an accuracy of 0.93; for fibroglandular tissue segmentation, the mean DSC was 0.67 with an accuracy of 0.75. The percent density calculated from ground truth and network segmentations were correlated, and showed a high coefficient of r=0.9. The initial results are promising, suggesting deep learning has a potential to provide an efficient and reliable breast density segmentation tool.