Hyperspectral remote sensing sensors have the ability to capture a wide range of spectrum of ground objects with hundreds to thousands of bands. The obtained hyperspectral images contain more detailed spectral information than conventional panchromatic or color images. However, redundant and noisy data could also be introduced into the images and may impair further processing of the data. Removing the redundancy and noisy bands becomes one of the most important preprocessing steps of hyperspectral imaging. As a feature selection method, an attention mechanism has been successfully used in computer vision and natural language processing to enable algorithms to concentrate on the most significant data. In this article, we propose a band attention network for hyperspectral image classification. This network can automatically learn to attend to the desired band set that maximizes the classification accuracy. With careful design, the band attention framework can undertake both band weighting and band selection tasks. When working in the band weighting mode, the proposed band attention framework can learn a band weighting vector that models the relationship between all the bands. For band selection, our network can be adapted as two different types of band selection networks that select the significant bands and discard the useless bands. In both tasks, the attention and classification can be learned end to end. The experimental results prove the effectiveness and advantages of the proposed work.