Few shot classification is a hot topic in the field of deep learning, which aims at identifying novel concepts with little supervisory information. In the remote sensing (RS) scene few shot classification, existing methods are often unable to achieve satisfactory accuracy because the relationships among samples are ignored. To improve the RS few shot classification accuracy, the multi-graph convolutional network (Multi-GCN) is proposed in this paper. In the proposed method, a graph convolutional network is introduced into the metric network to smooth the samples’ features, which can model relationships among samples, make images from the same class get more similar feature representation and improve the classification accuracy. The proposed Multi-GCN is mainly composed of three parts: (1) Feature extraction network, which is composed of 4-layer convolutional neural networks and is used to extract images’ features; (2) Graph convolutional network, which is used to model the relationships among samples in the feature space, and update the node features by multi-graph convolution; (3) Metric prediction part, which is used to calculate the prototype of each class, and predict labels of the unlabeled samples according to the distance between samples and prototypes. Based on spectral domain analysis, the proposed multi-graph convolution can effectively suppress the high-frequency components of the graph signals and significantly enhance the clustering coefficients of features from the same class. In addition, the fine-tuning method is introduced in the training process, and labeled samples in the new class are used to train the last layer of the graph convolutional network for a small number of steps, which can further improve the classification accuracy and enhance the transfer ability of the model. To validate the effectiveness of the proposed method, in the experiments, Multi-GCN is compared with ProtoNet, GNN-FSL, and two single graph based methods ProtoGCN and ProtoIGCN on two different tasks, i.e. the same dataset few shot classification task and cross datasets few shot classification task. From the experimental results, we can obtain that in the same dataset few shot classification task, the proposed method is significantly superior to ProtoNet. When the number of labeled samples of each class is 1, the accuracy of the proposed method is higher than ProtoNet by more than 5%; Compared with GNN-FSL, the accuracy of the proposed method is about 10% higher on average. In the cross datasets few shot classification task, the classification accuracy of the proposed method is 10%—15% higher than that of GNN-FSL; And compared with ProtoNet, it is about 10% higher in the case of 1-shot and about 2%—5% higher in the case of 5-shot. In most cases, Multi-GCN is also better than single graph methods, such as ProtoGCN and ProtoIGCN. The classification accuracy can be further improved by using fine-tuning training methods. From the above experimental results, we can conclude that the proposed method can achieve a higher classification accuracy compared with ProtoNet, GNN-FSL, and the methods based on a single graph convolutional network. The conclusions of multi-graph convolutional operation and spectrum analysis in this work can also be extended to other graph-based semi-supervised learning.