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Currently, most scene classification algorithms are trained and evaluated based on a single dataset. However, practical applications are not usually restricted to specific satellite platforms or datasets. Researchers generally train a model on one dataset and require the model to perform tasks with another dataset, leading to a data shift problem and performance decrease in practical applications. To address this problem, this study presents a metric-based few-shot classification method with L 2 -norm prototypical networks. Specifically, a carefully designed L 2 -norm layer was introduced into prototypical networks. The proposed L 2 -norm layer applies L 2 -norm operations to prototypes and query features to mitigate the length fluctuations caused by the data shift problem. With this layer, the L 2 -norm prototypical networks maintain the ability to identify novel classes and limit the effects of data discrepancies. The proposed L 2 -norm layer improves the classification accuracy by 0.42% to 2.41% on various public datasets. Moreover, L 2 -norm prototypical networks outperform other methods by 0.02% to 34.38%. Comprehensive experiments consistently demonstrate the advantages of the proposed method in tackling the data shift problem. [ABSTRACT FROM AUTHOR]