Mammographic breast percent density (PD) is one of the strongest risk factors associated with the development of breast cancer. As a result, the accurate estimation of PD from screening mammograms is an important problem for breast cancer risk assessment. Nevertheless, automatic segmentation of the dense fibroglandular tissue (FGT) is a difficult task due to the complexity of morphological characteristics and heterogeneity of the breast. In this work, we present a hybrid algorithm based on convolutional neural networks (CNN) and intensity-based clustering used for the fully-automated segmentation of dense tissue in mammograms. We utilize a dataset of 582 mammograms with expert reader's manually segmented dense tissue areas as a reference. The PD estimates obtained with the proposed method yield a median PD error of 7.7% with no statistically significant differences with respect to the expert. The proposed method is also compared to a clinically validated algorithm