Diabetic Retinopathy (DR) is ranked at the top of blindness causes. It progresses without subjective symptoms and leads to blindness in the worst case. However early detections and proper treatments can prevent visual disturbance. Because it takes time and cost for diagnoses by clinicians, research and development of diagnostic support systems has actively been conducted. This research aims to establish a fundus image classification method based on disease severity assessment for a diagnostic support by a fundus image analysis. In this paper, we propose a Graph Neural Network (GNN)-based method to improve accuracy for severity classification. Our method has two features. The first is to extract Region-Of-Interest (ROI) sub-images focusing on regions locally capturing lesions in order to minimize background noise in image preprocessing for the classification. The second is to utilize the GNN which is not yet applied for fundus image classification. In order to evaluate our proposed method, we use Indian Diabetic Retinopathy Image Dataset (IDRiD) utilized in "Diabetic Retinopathy: Segmentation and Grading Challenge" on Biomedical Imaging held at the IEEE International Symposium in 2018. We verified that the accuracy of our method improved 2.9% over the conventional method in this contest.