Coronary artery calcium (CAC) is a significant marker of atherosclerosis and cardiovascular events. In this work we present a system for the automatic quantification of calcium score in ECG-triggered non-contrast enhanced cardiac computed tomography (CT) images. The proposed system uses a supervised deep learning algorithm, i.e. convolutional neural network (CNN) for the segmentation and classification of candidate lesions as coronary or not, previously extracted in the region of the heart using a cardiac atlas. We trained our network with 45 CT volumes; 18 volumes were used to validate the model and 56 to test it. Individual lesions were detected with a sensitivity of 91.24%, a specificity of 95.37% and a positive predicted value (PPV) of 90.5%; comparing calcium score obtained by the system and calcium score manually evaluated by an expert operator, a Pearson coefficient of 0.983 was obtained. A high agreement (Cohens k = 0.879) between manual and automatic risk prediction was also observed. These results demonstrated that convolutional neural networks can be effectively applied for the automatic segmentation and classification of coronary calcifications.