Chronic obstructive pulmonary disease (COPD) is a progressive lung dysfunction that can be triggered by exposure to chemicals. This disease can be identified with spirometry, but the patient feels uncomfortable, affecting the diagnosis results. Other disease markers are being investigated, including exhaled breath. This method can be applied easily, is non-invasive, has minimal side effects, and provides accurate results. This study applies the electronic nose method to distinguish healthy people and COPD suspects using exhaled breath samples. Twenty semiconductor gas sensors combined with machine learning algorithms were employed as an electronic nose system. Experimental results show that the frequency feature of the sensor responses used by the principal component analysis (PCA) method combined with graph convolutional network (GCN) can provide the highest accuracy value of 97.5% in distinguishing between healthy and COPD subjects. This method can improve the detection performance of electronic nose systems, which can help diagnose COPD.