Pulmonary segment segmentation is crucial for cancer localization and surgical planning. However, the pixel-wise annotation of pulmonary segments is laborious, as the boundaries between segments are indistinguishable in medical images. To this end, we propose a weakly supervised learning (WSL) method, termed Anatomy-Hierarchy Supervised Learning (AHSL), which consults the precise clinical anatomical definition of pulmonary segments to perform pulmonary segment segmentation. Since pulmonary segments reside within the lobes and are determined by the bronchovascular tree, i.e., artery, airway and vein, the design of the loss function is founded on two principles. First, segment-level labels are utilized to directly supervise the output of the pulmonary segments, ensuring that they accurately encompass the appropriate bronchovascular tree. Second, lobe-level supervision indirectly oversees the pulmonary segment, ensuring their inclusion within the corresponding lobe. Besides, we introduce a two-stage segmentation strategy that incorporates bronchovascular priori information. Furthermore, a consistency loss is proposed to enhance the smoothness of segment boundaries, along with an evaluation metric designed to measure the smoothness of pulmonary segment boundaries. Visual inspection and evaluation metrics from experiments conducted on a private dataset demonstrate the effectiveness of our method.