Accurate earthquake location and magnitude estimation play critical roles in seismology. Recent deep learning frameworks have produced encouraging results on various seismological tasks (e.g., earthquake detection, phase picking, seismic classification, and earthquake early warning). Most existing machine learning earthquake location methods utilize waveform information from a single station. However, multiple stations contain more complete information for earthquake source characterization. Inspired by recent successes in applying graph neural networks in graph-structured data, we develop a Spatio-Temporal Graph Convolutional Neural Network (STGCN) for estimating earthquake locations and magnitudes. Our graph neural network leverages geographical and waveform information from multiple stations to construct graphs automatically and dynamically by an adaptive feature integration process. Given input waveforms collected from multiple stations, the neural network constructs different graphs and fuses spatial-temporal consistency effectively from various stations based on graphs’ edges. Using a recent graph neural network and a fully convolutional neural network as baselines, we apply STGCN to earthquakes cataloged by Southern California Seismic Network from 2000 to 2019 and induced earthquakes collected in Oklahoma from 2014 to 2015. STGCN yields more accurate earthquake locations than those obtained by the baseline models and performs comparably in terms of depth and magnitude prediction, though the ability to predict depth and magnitude remains weak for all tested models. Our work demonstrates the potential of using graph neural networks and multiple stations for better automatic estimation of earthquake epicenters.