PURPOSE: Segmentation of left ventricular myocardium (LVM) in coronary computed tomography angiography (CCTA) is important for diagnosis of cardiovascular diseases. Due to poor image contrast and large variation in intensity and shapes, LVM segmentation for CCTA is a challenging task. The purpose of this work is to develop a region-based deep learning method to automatically detect and segment the LVM solely based on CCTA images. METHODS: We developed a 3D deeply supervised U-Net, which incorporates attention gates (AGs) to focus on the myocardial boundary structures, to segment LVM contours from CCTA. The deep attention U-Net (DAU-Net) was trained on the patients' CCTA images, with a manual contour-derived binary mask used as the learning-based target. The network was supervised by a hybrid loss function, which combined logistic loss and Dice loss to simultaneously measure the similarities and discrepancies between the prediction and training datasets. To evaluate the accuracy of the segmentation, we retrospectively investigated 100 patients with suspected or confirmed coronary artery disease (CAD). The LVM volume was segmented by the proposed method and compared with physician-approved clinical contours. Quantitative metrics used were Dice similarity coefficient (DSC), Hausdorff distance (HD), mean surface distance (MSD), residual mean square distance (RMSD), the center of mass distance (CMD), and volume difference (VOD). RESULTS: The proposed method created contours with very good agreement to the ground truth contours. Our proposed segmentation approach is benchmarked primarily using fivefold cross validation. Model prediction correlated and agreed well with manual contour. The mean DSC of the contours delineated by our method was 91.6% among all patients. The resultant HD was 6.840 ± 4.410 mm. The proposed method also resulted in a small CMD (1.058 ± 1.245 mm) and VOD (1.640 ± 1.777 cc). Among all patients, the MSD and RMSD were 0.433 ± 0.209 mm and 0.724 ± 0.375 mm, respectively, between ground truth and LVM volume resulting from the proposed method. CONCLUSIONS: We developed a novel deep learning-based approach for the automated segmentation of the LVM on CCTA images. We demonstrated the high accuracy of the proposed learning-based segmentation method through comparison with ground truth contour of 100 clinical patient cases using six quantitative metrics. These results show the potential of using automated LVM segmentation for computer-aided delineation of CADs in the clinical setting.