Deep learning plays an important role in solving the problem of remote sensing image scene classification. However, in certain remote sensing scene classification problems, samples with labels that can be trained are severely lacking (number of single-class samples less than 10), resulting in unsatisfactory classification using existing traditional depth models. In this paper, to solve these problems, a small-sample-size remote sensing scene classification method is proposed, and a model called ResNet14 Attention-ProtoNet (RA-ProtoNet) based on a meta-learning training strategy is constructed. First,in the feature embedding module, the pre-trained depth residual network, ResNet14, is used to extract the depth features of remote sensing images. Second, in the class-level expression module, the problem that the features of similar samples are unremarkable and interfere in class-level expressions is solved. For this purpose, an attention mechanism based on bidirectional long short-term memory (Bi-LSTM) is used to strengthen the sample information within a class and generate class-level feature expressions of samples. Finally, the Euclidean distance is used to measure the distances between the samples to be classified and the class-level features for classification prediction. On three remote sensing image datasets, including UCMERCED, AID-30 and NWPU-RESISC45, the proposed method is compared with remote sensing scene classification methods based on migration learning and existing meta-learning methods. Under the five-way five-shot condition, the overall scene classification accuracies of the proposed method reach 81.30%, 83.29%, and 81.22%, respectively. The experimental results show that the proposed method can effectively mine the sample information within a class and obtain higher classification accuracy of remote sensing image scenes under the condition of minimal samples than the other methods.