Autoencoder (AE) is an unsupervised neural network framework for efficient and effective feature extraction. Most AE-based methods do not consider spatial information and band correlations for hyperspectral image (HSI) analysis. In addition, graph-based AE methods often learn discriminative representations with the assumption that connected samples share the same label and they cannot directly embed the geometric structure into feature extraction. To address these issues, in this paper, we propose a dual graph autoencoder (DGAE) to learn discriminative representations for HSIs. Utilizing the relationships of pair-wise pixels within homogenous regions and pair-wise spectral bands, DGAE first constructs the superpixel-based similarity graph with spatial information and band-based similarity graph to characterize the geometric structures of HSIs. With the developed dual graph convolution, more discriminative feature representations are learnt from the hidden layer via the encoder-decoder structure of DGAE. The main advantage of DGAE is that it fully exploits both the geometric structures of pixels with spatial information and spectral bands to promote nonlinear feature extraction of HSIs. Experiments on HSI datasets show the superiority of the proposed DGAE over the state-of-the-art methods.