Breast cancer is the leading cause of death for women in most countries. The high levels of mortality relate mostly to late diagnosis and to the direct proportionally relationship between breast density and breast cancer development. Therefore, the correct assessment of breast density is important to provide better screening for higher risk patients. However, in modern digital mammography the discrimination among breast densities is highly complex due to increased contrast and visual information for all densities. Thus, a computational system for classifying breast density might be a useful tool for aiding medical staff. Several machine-learning algorithms are already capable of classifying small number of classes with good accuracy. However, machinelearning algorithms main constraint relates to the set of features extracted and used for classification. Although well-known feature extraction techniques might provide a good set of features, it is a complex task to select an initial set during design of a classifier. Thus, we propose feature extraction using a Convolutional Neural Network (CNN) for classifying breast density by a usual machine-learning classifier. We used 307 mammographic images downsampled to 260x200 pixels to train a CNN and extract features from a deep layer. After training, the activation of 8 neurons from a deep fully connected layer are extracted and used as features. Then, these features are feedforward to a single hidden layer neural network that is cross-validated using 10-folds to classify among four classes of breast density. The global accuracy of this method is 98.4%, presenting only 1.6% of misclassification. However, the small set of samples and memory constraints required the reuse of data in both CNN and MLP-NN, therefore overfitting might have influenced the results even though we cross-validated the network. Thus, although we presented a promising method for extracting features and classifying breast density, a greater database is still required for evaluating the results.