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Transformer-based networks, which can well model global characteristics of inputted data using attention mechanism, have been widely applied to hyperspectral image (HSI) classification and achieved promising results. However, existing networks fail to explore complex local land cover structures in different scales of shapes in hyperspectral remote sensing images. Therefore, a novel network named multi-scale and cross-level attention learning (MCAL) network is proposed to fully explore both global and local multi-scale features of pixels for classification. In order to encounter local spatial context of pixels in transformer, a multi-scale feature extraction module (MSFE) is constructed and implemented into transformer-based networks. Moreover, a cross-level feature fusion module (CLFF) is proposed to adaptively fuse features from hierarchical structure of MSFEs using attention mechanism. Finally, the spectral attention module is implemented prior to the hierarchical structure of MSFEs, by which both spatial context and spectral information are jointly emphasized for hyperspectral classification. Experiments over several benchmark datasets demonstrate that the proposed MCAL obviously outperforms both CNN-based and transformer-based state-of-the-art networks for hyperspectral classification.