Hyperspectral remote sensing images use hundreds of bands to describe the fine spectral information of the ground area. However, they inevitably contain a large amount of redundancy as well as noisy bands. Discovering the most informative bands and modeling the relationship among the bands are effective means to process the data and improve the performance of the subsequent classification task. Attention mechanism is used in computer vision and natural language processing to guide the algorithm towards the most relevant information in the data. In this paper, we propose a band weighting network by designing and integrating an attention module in the traditional convolutional neural network for hyperspectral image classification. Our proposed band weighting network has the capability to model the relationship among the bands and weight them according to their joint contribution to classification. One prominent feature of our proposed method is that it can assign different weights to different samples. The experimental results demonstrate the effectiveness and superiority of our approach.