Convolutional neural network (CNN) based methods have dominated the field of aerial scene classification for the past few years. While achieving remarkable success, CNN-based methods suffer from excessive parameters and notoriously rely on large amounts of training data. In this work, we introduce few-shot learning to the aerial scene classification problem. Few-shot learning aims to learn a model on base-set that can quickly adapt to unseen categories in novel-set, using only a few labeled samples. To this end, we proposed a meta-learning method for few-shot classification of aerial scene images. First, we train a feature extractor on all base categories to learn a representation of inputs. Then in the meta-training stage, the classifier is optimized in the metric space by cosine distance with a learnable scale parameter. At last, in the meta-testing stage, the query sample in the unseen category is predicted by the adapted classifier given a few support samples. We conduct extensive experiments on two challenging datasets: NWPU-RESISC45 and RSD46-WHU. The experimental results show that our method yields state-of-the-art performance. Furthermore, several ablation experiments are conducted to investigate the effects of dataset scale, the impact of different metrics and the number of support shots; the experiment results confirm that our model is specifically effective in few-shot settings.