The purpose of this study was to develop a fully automated algorithm for mammographic breast density estimation using deep learning. Our algorithm used a fully convolutional network, which is a deep learning framework for image segmentation, to segment both the breast and the dense fibroglandular areas on mammographic images. Using the segmented breast and dense areas, our algorithm computed the breast percent density (PD), which is the faction of dense area in a breast. Our dataset included full-field digital screening mammograms of 604 women, which included 1208 mediolateral oblique (MLO) and 1208 craniocaudal (CC) views. We allocated 455, 58, and 91 of 604 women and their exams into training, testing, and validation datasets, respectively. We established ground truth for the breast and the dense fibroglandular areas via manual segmentation and segmentation using a simple thresholding based on BI-RADS density assessments by radiologists, respectively. Using the mammograms and ground truth, we fine-tuned a pretrained deep learning network to train the network to segment both the breast and the fibroglandular areas. Using the validation dataset, we evaluated the performance of the proposed algorithm against radiologists' BI-RADS density assessments. Specifically, we conducted a correlation analysis between a BI-RADS density assessment of a given breast and its corresponding PD estimate by the proposed algorithm. In addition, we evaluated our algorithm in terms of its ability to classify the BI-RADS density using PD estimates, and its ability to provide consistent PD estimates for the left and the right breast and the MLO and CC views of the same women. To show the effectiveness of our algorithm, we compared the performance of our algorithm against a state of the art algorithm, laboratory for individualized breast radiodensity assessment (LIBRA). The PD estimated by our algorithm correlated well with BI-RADS density ratings by radiologists. Pearson's rho values of our algorithm for CC view, MLO view, and CC-MLO-averaged were 0.81, 0.79, and 0.85, respectively, while those of LIBRA were 0.58, 0.71, and 0.69, respectively. For CC view and CC-MLO averaged cases, the difference in rho values between the proposed algorithm and LIBRA showed statistical significance (P<0.006). In addition, our algorithm provided reliable PD estimates for the left and the right breast (Pearson's ρ>0.87) and for the MLO and CC views (Pearson's ρ=0.76). However, LIBRA showed a lower Pearson's rho value (0.66) for both the left and right breasts for the CC view. In addition, our algorithm showed an excellent ability to separate each sub BI-RADS breast density class (statistically significant, p-values = 0.0001 or less); only one comparison pair, density 1 and density 2 in the CC view, was not statistically significant (P=0.54). However, LIBRA failed to separate breasts in density 1 and 2 for both the CC and MLO views (P>0.64). We have developed a new deep learning based algorithm for breast density segmentation and estimation. We showed that the proposed algorithm correlated well with BI-RADS density assessments by radiologists and outperformed an existing state of the art algorithm.