Alzheimer's disease (AD), the most prevalent degenerative brain disease associated with dementia, requires early diagnosis to alleviate worsening of symptoms through appropriate management and treatment. Recent studies on AD stage classification are increasingly using multimodal data. However, few studies have applied graph neural networks to multimodal data comprising F-18 florbetaben (FBB) amyloid brain positron emission tomography (PET) images and clinical indicators. The objective of this study was to demonstrate the effectiveness of graph convolutional network (GCN) for AD stage classification using multimodal data, specifically FBB PET images and clinical indicators, collected from Dong-A University Hospital (DAUH) and Alzheimer's Disease Neuroimaging Initiative (ADNI). The effectiveness of GCN was demonstrated through comparisons with the support vector machine, random forest, and multilayer perceptron across four classification tasks (normal control (NC) vs. AD, NC vs. mild cognitive impairment (MCI), MCI vs. AD, and NC vs. MCI vs. AD). As input, all models received the same combined feature vectors, created by concatenating the PET imaging feature vectors extracted by the 3D dense convolutional network and non-imaging feature vectors consisting of clinical indicators using multimodal feature fusion method. An adjacency matrix for the population graph was constructed using cosine similarity or the Euclidean distance between subjects' PET imaging feature vectors and/or non-imaging feature vectors. The usage ratio of these different modal data and edge assignment threshold were tuned by setting them as hyperparameters. In this study, GCN-CS-com and GCN-ED-com were the GCN models that received the adjacency matrix constructed using cosine similarity (CS) and the Euclidean distance (ED) between the subjects' PET imaging feature vectors and non-imaging feature vectors, respectively. In modified nested cross validation, GCN-CS-com and GCN-ED-com respectively achieved average test accuracies of 98.40%, 94.58%, 94.01%, 82.63% and 99.68%, 93.82%, 93.88%, 90.43% for the four aforementioned classification tasks using DAUH dataset, outperforming the other models. Furthermore, GCN-CS-com and GCN-ED-com respectively achieved average test accuracies of 76.16% and 90.11% for NC vs. MCI vs. AD classification using ADNI dataset, outperforming the other models. These results demonstrate that GCN could be an effective model for AD stage classification using multimodal data.