Unsupervised band selection aims to select informative spectral bands to preprocess hyperspectral images (HSIs) without using labels. Traditional band selection methods only work well on Euclidean data, but ignore structural information of pixels and spectral bands. Moreover, they treat each HSI as a whole to exploit latent spatial information while ignoring the difference in spatial distribution between diverse homogeneous regions. In this article, we propose a robust dual graph self-representation (RDGSR) method for unsupervised band selection. RDGSR uses a superpixel segmentation technique to generate homogenous regions of each HSI to extract spatial information. Based on the segmentation result, the superpixel-based similarity graph and band-based similarity graph are constructed from HSIs to record spatial and structural information. With this knowledge, the dual graph convolution is developed and the ℓ2,1 -norm is introduced in the loss function and regularization term to eliminate the noise in rows for robust and effective band selection. The novelty of RDGSR is the joint utilization of the geometric structure of pixels with spatial consistency and the geometric structure of spectral bands to enhance the performance of band selection in a robust ℓ 2,1 -norm manner. An iterative optimization algorithm is designed to solve the proposed formulation. Substantial experiments on HSI datasets are conducted to verify the superiority of the proposed RDGSR over the state-of-the-art methods. The source code is available at https://github.com/ZhangYongshan/RDGSR.