Reorganizing implicit feedback of users as a user-item interaction graph facilitates the applications of graph convolutional networks (GCNs) in recommendation tasks. In the interaction graph, edges between user and item nodes function as the main element of GCNs to perform information propagation and generate informative representations. Nevertheless, an underlying challenge lies in the quality of interaction graph, since observed interactions with lessinterested items occur in implicit feedback (say, a user views micro-videos accidentally). This means that the neighborhoods involved with such false-positive edges will be influenced negatively and the signal on user preference can be severely contaminated. However, existing GCN-based recommender models leave such challenge under-explored, resulting in suboptimal representations and performance.In this work, we focus on adaptively refining the structure of interaction graph to discover and prune potential false-positive edges. Towards this end, we devise a new GCN-based recommender model, Graph-Refined Convolutional Network (GRCN), which adjusts the structure of interaction graph adaptively based on status of model training, instead of remaining the fixed structure. In particular, a graph refining layer is designed to identify the noisy edges with the high confidence of being false-positive interactions, and consequently prune them in a soft manner. We then apply a graph convolutional layer on the refined graph to distill informative signals on user preference. Through extensive experiments on three datasets for micro-video recommendation, we validate the rationality and effectiveness of our GRCN. Further in-depth analysis presents how the refined graph benefits the GCNbased recommender model.