Deep neural networks have achieved great success in image classification tasks based on a large amount of training data, but still lack the capability of learning to recognize new categories with few training instances, which is the setting of few-shot learning. In this paper, we propose a new end-to-end few-shot metric learning approach named Graph Embedding Relation Network (GERN), with a shallow and a deep variant. By learning the embeddings of images, employing Graph Neural Network (GNN) and using embedding concatenations, GERNs can construct stronger inter-class and intra-class relations between images, which improves models’ performances. Comprehensive experiments on miniImageNet and tieredImageNet demonstrate that compared with existing few-shot metric learning approaches, GERN has made significant improvements on one-shot and few-shot classification, and has achieved highly competitive performances compared with several state-of-the-art approaches.