Abstract: Learning node embedding that captures the position of the node within a broader graph structure is crucial for many prediction tasks on graphs. However, while expressive and most popular, existing Graph Neural Network (GNN) approaches have limited power for representing positions/locations of nodes in a bigger network structure. Here we propose {\em Position-aware Graph Neural Networks (P-GNN)}, a new class of GNNs for computing position-aware node embeddings. P-GNN first selects a set of anchor nodes, characterizes the distance of a given target node towards the anchor-set, and then learns a non-linear aggregation scheme over the anchor-sets adjacent to the target node. P-GNN has several advantages: it is inductive, scalable, and can incorporate node feature information. We apply P-GNNs to multiple prediction tasks including link prediction and community detection. We show that P-GNNs consistently outperform state of the art GNN variants, with an improvement up to $38\%$ in terms of AUC score.