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Despite recent advances in Graph Neural Networks (GNNs), their training strategies remain largely under-explored. The conventional training strategy learns over all nodes in the original graph(s) equally, which can be sub-optimal as certain nodes are often more difficult to learn than others. Here we present TuneUp, a simple curriculum-based training strategy for improving the predictive performance of GNNs. TuneUp trains a GNN in two stages. In the first stage, TuneUp applies conventional training to obtain a strong base GNN. The base GNN tends to perform well on head nodes (nodes with large degrees) but less so on tail nodes (nodes with small degrees). Therefore, the second stage of TuneUp focuses on improving prediction on the difficult tail nodes by further training the base GNN on synthetically generated tail node data. We theoretically analyze TuneUp and show it provably improves generalization performance on tail nodes. TuneUp is simple to implement and applicable to a broad range of GNN architectures and prediction tasks. Extensive evaluation of TuneUp on five diverse GNN architectures, three types of prediction tasks, and both transductive and inductive settings shows that TuneUp significantly improves the performance of the base GNN on tail nodes, while often even improving the performance on head nodes. Altogether, TuneUp produces up to 57.6% and 92.2% relative predictive performance improvement in the transductive and the challenging inductive settings, respectively.