Image matching is a key component of many tasks in computer vision and its main objective is to find correspondences between features extracted from different natural images. When images are represented as graphs, image matching boils down to the problem of graph matching which has been studied intensively in the past. In recent years, graph neural networks have shown great potential in the graph matching task, and have also been applied to image matching. In this paper, we propose a graph neural network for the problem of image matching. The proposed method first generates initial soft correspondences between keypoints using localized node embeddings and then iteratively refines the initial correspondences using a series of graph neural network layers. We evaluate our method on natural image datasets with keypoint annotations and show that, in comparison to a state-of-the-art model, our method speeds up inference times without sacrificing prediction accuracy.