Forecasting influenza-like illness (ILI) is of prime importance to epidemiologists and health-care providers. Early prediction of epidemic outbreaks plays a pivotal role in disease intervention and control. Most existing work has either limited long-term prediction performance or fails to capture spatio-temporal dependencies in data. In this paper, we design a cross-location attention based graph neural network (Cola-GNN) for learning time series embeddings in long-term ILI predictions. We propose a graph message passing framework to combine graph structures (e.g., geolocations) and time-series features (e.g., temporal sequences) in a dynamic propagation process. We compare the proposed method with state-of-the-art statistical approaches and deep learning models. We conducted a set of extensive experiments on real-world epidemic-related datasets from the United States and Japan. The proposed method demonstrated strong predictive performance and leads to interpretable results for long-term epidemic predictions.