Geospatial artificial intelligence (GeoAI) has emerged as a subfield of GIScience that uses artificial intelligence approaches and machine learning techniques for geographic knowledge discovery. The non-regularity of data structures has recently led to different variants of graph neural networks in the field of computer science, with graph convolutional neural networks being one of the most prominent that operate on non-euclidean structured data where the numbers of nodes connections vary and the nodes are unordered. These networks use graph convolution – commonly known as filters or kernels – in place of general matrix multiplication in at least one of their layers. This paper suggests spatial regression graph convolutional neural networks (SRGCNNs) as a deep learning paradigm that is capable of handling a wide range of geographical tasks where multivariate spatial data needs modeling and prediction. The feasibility of SRGCNNs lies in the feature propagation mechanisms, the spatial locality nature, and a semi-supervised training strategy. In the experiments, this paper demonstrates the operation of SRGCNNs with social media check-in data in Beijing and house price data in San Diego. The results indicate that a well-trained SRGCNN model is capable of learning from samples and performing reasonable predictions for unobserved locations. The paper also presents the effectiveness of incorporating the idea of geographically weighted regression for handling heterogeneity between locations in the model approach. Compared to conventional spatial regression approaches, SRGCNN-based models tend to generate much more accurate and stable results, especially when the sampling ratio is low. This study offers to bridge the methodological gap between graph deep learning and spatial regression analytics. The proposed idea serves as an example to illustrate how spatial analytics can be combined with state-of-the-art deep learning models, and to enlighten future research at the front of GeoAI.