Recent studies in human brain connectomics have widely reported brain connectivity abnormalities associated with schizophrenia. However, most previous discriminative studies of SZ patients using machine learning methods were based on MRI features of brain regions, ignoring brain connectivity and its network topology. We addressed these limitations by applying a graph convolutional network (GCN) to classify schizophrenia patients with brain region and connectivity features derived from a combined functional MRI and connectomics analysis. In this study, 140 schizophrenia patients and 205 normal controls were included, and resting-state functional magnetic resonance imaging (rs-fMRI) data were acquired for each subject. Brain region features, including the amplitude of low-frequency fluctuation (ALFF), regional homogeneity (ReHo), and degree centrality (DC), were computed by MRI analysis and connectomics analysis, respectively. Moreover, brain connectivity features were explored by connectomics analysis. A GCN method was proposed to learn network representations to discrimi-nate patients with schizophrenia from normal controls. Compared with the traditional machine learning and deep learning methods based on MRI features of brain regions, the proposed method based on a combined functional MRI and connectomics analysis can effectively improve classification performance. Specifically, we obtained an average accuracy of 92.47%, and the area under the curve (AUC), sensitivity, specificity, precision and F1-score reached 95.36%, 88.70%, 95.06%, 92.87%, and 90.45%, respectively. These findings indicated that GCN based on brain connectivity and network topology is a promising method to improve the classification performance of schizophrenia patients.