obstructive pulmonary disease (COPD) is a prevalent chronic disease with high morbidity and mortality. The early diagnosis of COPD is vital for clinical treatment, which helps patients to have a better quality of life. Because COPD can be ascribed to chronic bronchitis and emphysema, lesions in a computed tomography (CT) image can present anywhere inside the lung with different types, shapes and sizes. Multiple instance learning (MIL) is an effective tool for solving COPD discrimination. In this study, a novel graph convolutional MIL with the adaptive additive margin loss (GCMIL-AAMS) approach is proposed to diagnose COPD by CT. Specifically, for those early stage patients, the selected instance-level features can be more discriminative if they were learned by our proposed graph convolution and pooling with self-attention mechanism. The AAMS loss can utilize the information of COPD severity on a hypersphere manifold by adaptively setting the angular margins to improve the performance, as the severity can be quantified as four grades by pulmonary function test. The results show that our proposed GCMIL-AAMS method provides superior discrimination and generalization abilities in COPD discrimination, with areas under a receiver operating characteristic curve (AUCs) of 0.960 +/- 0.014 and 0.862 +/- 0.010 in the test set and external testing set, respectively, in 5-fold stratified cross validation; moreover, it demonstrates that graph learning is applicable to MIL and suggests that MIL may be adaptable to graph learning.