This paper introduces a novel approach to classify pulmonary arteries and veins from volumetric chest computed tomography (CT) images. Although there is known to be a relationship between the alteration of vessel distributions and the progress of various pulmonary diseases, there has been relatively little research on the quantification of pulmonary vessels in vivo due to morphological difficulties. In particular, there have been few efforts to quantify the morphology and distribution of only arteries or veins through automated algorithms despite the clinical importance of such work. In this study, the authors classify different types of vessels by constructing a tree structure from vascular points while minimizing the construction cost using the vascular geometries and features of CT images. First, a vascular point set is extracted from an input volume and the weights of the points are calculated using the intensity, distance from the boundaries, and the Laplacian of the distance field. The tree construction cost is then defined as the summation of edge connection costs depending on the vertex weights. As a solution, the authors can obtain a minimum spanning tree whose branches correspond to different vessels. By cutting the edges in the mediastinal region, branches can be separated. From the root points of each branch, the cut region is regrouped toward the entries of pulmonary vessels in the same framework of the initial tree construction. After merging branches with the same orientation as much as possible, it can be determined manually whether a given vessel is an artery or vein. Our approach can handle with noncontrast CT images as well as vascular contrast enhanced images. For the validation, mathematical virtual phantoms and ten chronic obstructive pulmonary disease (COPD) noncontrast volumetric chest CT scans with submillimeter thickness were used. Based on experimental findings, the suggested approach shows 9.18 ± 0.33 (mean ± SD) visual scores for ten datasets, 91% and 98% quantitative accuracies for two cases, a result which is clinically acceptable in terms of classification capability. This automatic classification approach with minimal user interactions may be useful in assessing many pulmonary disease, such as pulmonary hypertension, interstitial lung disease and COPD.