Background: It is fundamental for accurate segmentation and quantification of the pulmonary vessel, particularly smaller vessels, from computed tomography (CT) images in chronic obstructive pulmonary disease (COPD) patients. Objective: The aim of this study was to segment the pulmonary vasculature using a semi-supervised method. Methods: In this study, a self-training framework is proposed by leveraging a teacher-student model for the segmentation of pulmonary vessels. First, the high-quality annotations are acquired in the in-house data by an interactive way. Then, the model is trained in the semi-supervised way. A fully supervised model is trained on a small set of labeled CT images, yielding the teacher model. Following this, the teacher model is used to generate pseudo-labels for the unlabeled CT images, from which reliable ones are selected based on a certain strategy. The training of the student model involves these reliable pseudo-labels. This training process is iteratively repeated until an optimal performance is achieved. Results: Extensive experiments are performed on non-enhanced CT scans of 125 COPD patients. Quantitative and qualitative analyses demonstrate that the proposed method, Semi2, significantly improves the precision of vessel segmentation by 2.3%, achieving a precision of 90.3%. Further, quantitative analysis is conducted in the pulmonary vessel of COPD, providing insights into the differences in the pulmonary vessel across different severity of the disease. Conclusion: The proposed method can not only improve the performance of pulmonary vascular segmentation, but can also be applied in COPD analysis. The code will be made available at https://github.com/wuyanan513/semi-supervised-learning-for-vessel-segmentation.