Skeleton-based human action recognition is becoming increasingly important in a variety of fields. Most existing works train a CNN or GCN based backbone to extract spatial-temporal features, and use temporal average/max pooling to aggregate the information. However, these pooling methods fail to capture high-order dynamics information. To address the problem, we propose a plug-and-play module called Koopman pooling, which is a parameterized high-order pooling technique based on Koopman theory. The Koopman operator linearizes a non-linear dynamics system, thus providing a way to represent the complex system through the dynamics matrix, which can be used for classification. We also propose an eigenvalue normalization method to encourage the learned dynamics to be non-decaying and stable. Besides, we also show that our Koopman pooling framework can be easily extended to one-shot action recognition when combined with Dynamic Mode Decomposition. The proposed method is evaluated on three benchmark datasets, namely NTU RGB+D 60, 120 and NW-UCLA. Our experiments clearly demonstrate that Koopman pooling significantly improves the performance under both full-dataset and one-shot settings.