Event prediction tasks often handle spatio-temporal data distributed in a large spatial area. Different regions in the area exhibit different characteristics while having latent correlations. This spatial heterogeneity and correlations greatly affect the spatio-temporal distributions of event occurrences, which has not been addressed by state-of-the-art models. Learning spatial dependencies of events in a continuous space is challenging due to its fine granularity and a lack of prior knowledge. In this work, we propose a novel Graph Spatio-Temporal Point Process (GSTPP) model for fine-grained event prediction. It adopts an encoder-decoder architecture that jointly models the state dynamics of spatially localized regions using neural Ordinary Differential Equations (ODEs). The state evolution is built on the foundation of a novel Self-Adaptive Anchor Graph (SAAG) that captures spatial dependencies. By adaptively localizing the anchor nodes in the space and jointly constructing the correlation edges between them, the SAAG enhances the model's ability of learning complex spatial event patterns. The proposed GSTPP model greatly improves the accuracy of fine-grained event prediction. Extensive experimental results show that our method greatly improves the prediction accuracy over existing spatio-temporal event prediction approaches.