Metric learning methods are widely used in few-shot learning due to their simplicity and effectiveness. Most existing methods directly predict query labels by comparing the similarity between support and query samples. In this paper, we design a cycle optimization metric network for few-shot classification task that optimizes model performance based on loop-prediction of the labels of query samples and support samples. Specifically, we construct a forward network and reverse network based on a geometric algebra Graph Neural Network (GA-GNN). These two networks form the loop prediction from support samples to query samples and then back to support samples, guided by a cycle-consistency loss. We also introduce an optimization module that is able to correct the predicted results of query samples to further improve the network performance. Our extensive experimental results demonstrate that the proposed cycle optimization metric network outperforms existing state-of-the-art few-shot learning methods on classification tasks.