In few-shot image classification tasks, capturing remote semantic information in feature extraction modules based on convolutional neural network and single measure of edge-feature similarity are challenging. Therefore, in this study, we present a few-shot image classification method utilizing a graph neural network based on Swin Transformer. First, the Swin Transformer is used to extract image features, which are utilized as node features in the graph neural network. Next, the edge-feature similarity measurement module is improved by adding additional metrics, thus forming a dual-measurement module to calculate the similarity between the node features. The obtained similarity is used as the edge-feature input of the graph neural network. Finally, the nodes and edges of the graph neural network are alternately updated to predict image class labels. The classification accuracy of our proposed method for a 5-way 1-shot task on Stanford Dogs, Stanford Cars, and CUB-200-2011 datasets is calculated as 85.21%, 91.10%, and 91.08%, respectively, thereby achieving significant results in few-shot image classification.