This study presents an automatic method for 3D reconstruction of vascular trees using computed-tomography angiographic (CTA) images. The program starts with the CTA slices, performs a sequential procedure of 3D image formation, preprocessing, segmentation, thinning, skeleton pruning and tree construction. It ends with vascular trees along with quantitative data about the trees such as values of diameter, length and bifurcation angles. All the involved algorithms are presented with the emphasis given to the skeleton pruning and tree construction algorithms. The skeletons obtained using a 3D thinning algorithm may contain cycles, spurs, isolated sticks, and non-unit-width parts, which hinder tree construction. As a solution to this problem, a skeleton pruning and tree construction algorithm is proposed. At each stage of the automatic procedure, 3D rendering is provided for visual inspection of the computed results. In the final output, the constructed vascular trees are visualized by rendering the 3D trees and the 3D binary image together in a transparent display mode. The program is carried out in a fully automatic fashion, with a few default settings. Occasionally, user intervention is needed at the 3D segmentation stage to impose an appropriate threshold when the automatic 3D segmentation is obviously sub-optimal for vessel delineation. Experimental demonstrations on both coronary artery phantom and a cast of coronary artery tree of a swine animal model are provided.