Graph-based fraud detection approaches have escalated lots of attention recently due to the abundant relational information of graph-structured data, which may be beneficial for the detection of fraudsters. However, the GNN-based algorithms could fare poorly when the label distribution of nodes is heavily skewed, and it is common in sensitive areas such as financial fraud, etc. To remedy the class imbalance problem of graph-based fraud detection, we propose a Pick and Choose Graph Neural Network (PC-GNN for short) for imbalanced supervised learning on graphs. First, nodes and edges are picked with a devised label-balanced sampler to construct sub-graphs for mini-batch training. Next, for each node in the sub-graph, the neighbor candidates are chosen by a proposed neighborhood sampler. Finally, information from the selected neighbors and different relations are aggregated to obtain the final representation of a target node. Experiments on both benchmark and real-world graph-based fraud detection tasks demonstrate that PC-GNN apparently outperforms state-of-the-art baselines.