Automated segmentation of three-dimensional medical images is of great importance for the detection and quantification of certain diseases such as stenosis in the coronary arteries. Many 2D and 3D deep learning models, especially deep convolutional neural networks (CNNs), have achieved state-of-the-art segmentation performance on 3D medical images. Yet, there is a trade-off between the field of view and the utilization of inter-slice information when using pure 2D or 3D CNNs for 3D segmentation, which compromises the segmentation accuracy. In this paper, we propose a two-stage strategy that retains the advantages of both 2D and 3D CNNs and apply the method for the segmentation of the human aorta and coronary arteries, with stenosis, from computed tomography (CT) images. In the first stage, a 2D CNN, which can extract large-field-of-view information, is used to segment the aorta and coronary arteries simultaneously in a slice-by-slice fashion. Then, in the second stage, a 3D CNN is applied to extract the inter-slice information to refine the segmentation of the coronary arteries in certain subregions not resolved well in the first stage. We show that the 3D network of the second stage can improve the continuity between slices and reduce the missed detection rate of the 2D CNN. Compared with directly using a 3D CNN, the two-stage approach can alleviate the class imbalance problem caused by the large non-coronary artery (aorta and background) and the small coronary artery and reduce the training time because the vast majority of negative voxels are excluded in the first stage. To validate the efficacy of our method, extensive experiments are carried out to compare with other approaches based on pure 2D or 3D CNNs and those based on hybrid 2D-3D CNNs.