What target labels are most effective for graph neural network (GNN) training? In some applications where GNNs excel-like drug design or fraud detection, labeling new instances is expensive. We develop a data-efficient active sampling framework, ScatterSample, to train GNNs under an active learning setting. ScatterSample employs a sampling module termed DiverseUncertainty to collect instances with large uncertainty from different regions of the sample space for labeling. To ensure diversification of the selected nodes, DiverseUncertainty clusters the high uncertainty nodes and selects the representative nodes from each cluster. Our ScatterSample algorithm is further supported by rigorous theoretical analysis demonstrating its advantage compared to standard active sampling methods that aim to simply maximize the uncertainty and not diversify the samples. In particular, we show that ScatterSample is able to efficiently reduce the model uncertainty over the whole sample space. Our experiments on five datasets show that ScatterSample significantly outperforms the other GNN active learning baselines, specifically it reduces the sampling cost by up to 50% while achieving the same test accuracy.