Pedestrian trajectory prediction has emerged as a core component of human-robot interaction and autonomous driving. Fast and accurate prediction of surrounding pedestrians contributes to making decisions and improves safety and efficiency. However, pedestrians’ future trajectories will interact with their surrounding traffic participants. As the density of pedestrians increases, the complexity of such interactions also increases significantly, leading to an inevitable decrease in the accuracy of pedestrian trajectory prediction. To address this issue, we propose DenseKoopman, a plug-and-play framework for dense pedestrian trajectory prediction. Specifically, we introduce the Koopman operator theory to find an embedding space for a global linear approximation of a nonlinear pedestrian motion system. By encoding historical trajectories as linear state embeddings in the Koopman space, we transforms nonlinear trajectory data for pedestrians in dense scenes. This linearized representation greatly reduces the complexity of dense pedestrian trajectory prediction. Extensive experiments on pedestrian trajectory prediction benchmarks demonstrate the superiority of the proposed framework. We also conducted an analysis of the data transformation to explore how our DenseKoopman framework works with each validation method and uncovers motion patterns that may be hidden within the trajectory data. Code is available at https://github.com/lixianbang/DenseKoopman.