Clinical diagnosis and treatment of tumors are greatly complicated by their heterogeneity, and the subtype classification of cancer frequently plays a significant role in the subsequent treatment of tumors. Presently, the majority of studies rely far too heavily on gene expression data, omitting the enormous power of multi-omics fusion data and the potential for patient similarities. In this study, we created a gastric cancer subtype classification model called RRGCN based on residual graph convolutional network (GCN) using multi-omics fusion data and patient similarity network. Given the multi-omics data's high dimensionality, we built an artificial neural network Autoencoder (AE) to reduce the dimensionality of the data and extract hidden layer features. The model is then built using the feature data. In addition, we computed the correlation between patients using the Pearson correlation coefficient, and this relationship between patients forms the edge of the graph structure. Four graph convolutional network layers and two residual networks with skip connections make up RRGCN, which reduces the amount of information lost during transmission between layers and prevents model degradation. The results show that RRGCN significantly outperforms other classification methods with an accuracy as high as 0.87 when compared to four other traditional machine learning methods and deep learning models. In terms of subtype classification, RRGCN excels in all areas and has the potential to offer fresh perspectives on disease mechanisms and disease progression. It has the potential to be used for a broader range of disorders and to aid in clinical diagnosis.