Despite many advances in Graph Neural Networks (GNNs), their training strategies simply focus on minimizing a loss over nodes in a graph. However, such simplistic training strategies may be sub-optimal as they neglect that certain nodes are much harder to make accurate predictions on than others. Here we present TuneUp, a curriculum learning strategy for better training GNNs. Crucially, TuneUp trains a GNN in two stages. The first stage aims to produce a strong base GNN. Such base GNNs tend to perform well on head nodes (nodes with large degrees) but less so on tail nodes (nodes with small degrees). So, the second stage of TuneUp specifically focuses on improving prediction on tail nodes. Concretely, TuneUp synthesizes many additional supervised tail node data by dropping edges from head nodes and reusing the supervision on the original head nodes. TuneUp then minimizes the loss over the synthetic tail nodes to finetune the base GNN. TuneUp is a general training strategy that can be used with any GNN architecture and any loss, making TuneUp applicable to a wide range of prediction tasks. Extensive evaluation of TuneUp on two GNN architectures, three types of prediction tasks, and both inductive and transductive settings shows that TuneUp significantly improves the performance of the base GNN on tail nodes, while often even improving the performance on head nodes, which together leads up to 58.5% relative improvement in GNN predictive performance. Moreover, TuneUp significantly outperforms its variants without the two-stage curriculum learning, existing graph data augmentation techniques, as well as other specialized methods for tail nodes.