Due to the existence of noise and spectral redundancies in hyperspectral images (HSIs), the band selection (BS) is highly required and can be achieved through the attention mechanism. However, existing BS methods fail to consider global interaction between the spectral information and spatial information in a nonlinear fashion. In this letter, we propose an end-to-end unsupervised dual-attention reconstruction network for BS (DARecNet-BS). The proposed network employs a dual-attention mechanism, i.e., position attention module (PAM) and channel attention module (CAM), to recalibrate the feature maps and subsequently uses a 3-D reconstruction network to restore the original HSI. This way, the long-range nonlinear contextual information in spectral and spatial directions is captured, and the informative band subset can be selected. Experiments are conducted on three well-known hyperspectral data sets, i.e., Indian Pines (IP), University of Pavia (UP), and Salinas (SA), to compare existing BS approaches, and the proposed DARecNet-BS can effectively select less redundant bands with comparable or better classification accuracy. The source code will be made publicly available at https://github.com/ucalyptus/DARecNet-BS.