Stock trend prediction involves forecasting the future price movements by analyzing historical data and various market indicators. With the advancement of machine learning, graph neural networks (GNNs) have been extensively employed in stock prediction due to their powerful capability to capture spatiotemporal dependencies of stocks. However, despite the efforts of various GNN stock predictors to enhance predictive performance, the improvements remain limited, as they focus solely on analyzing historical spatiotemporal dependencies, overlooking the correlation between historical and future patterns. In this study, we propose a novel distillation-based future-aware GNN framework (DishFT-GNN) for stock trend prediction. Specifically, DishFT-GNN trains a teacher model and a student model, iteratively. The teacher model learns to capture the correlation between distribution shifts of historical and future data, which is then utilized as intermediate supervision to guide the student model to learn future-aware spatiotemporal embeddings for accurate prediction. Through extensive experiments on two real-world datasets, we verify the state-of-the-art performance of DishFT-GNN.