This article proposes a dual global–local attention network (DGLAnet), which is an end-to-end unsupervised band selection (UBS) method that fully utilizes spatial and spectral information in both global and local aspects. The DGLAnet assumes that BS can be realized using the hyperspectral image (HSI) reconstruction process. First, the DGLAnet implements a dual attention module to obtain spatial–spectral and global–local features to reweight the HSI data. It adopts bi-directional relations to grasp spatial and spectral features from a global perspective. Meanwhile, the DGLAnet extracts local features through max-pooling and mean-pooling and then merges them via the convolution operation. Global–local features are utilized to learn attention to recalibrate the original data, and the reconstruction module is adopted to restore the original image from the reweighted HSI data. Finally, a proper band subset is selected by the constructed band evaluation index. Experiments on three hyperspectral data show that the DGLAnet outperforms other state-of-the-art methods and uses all bands with a lower computational cost.