In this paper, we propose a spectral-spatial graph reasoning network (SSGRN) for hyperspectral image (HSI) classification. Concretely, this network contains two parts that separately named spatial graph reasoning subnetwork (SAGRN) and spectral graph reasoning subnetwork (SEGRN) to capture the spatial and spectral graph contexts, respectively. Different from the previous approaches implementing superpixel segmentation on the original image or attempting to obtain the category features under the guide of label image, we perform the superpixel segmentation on intermediate features of the network to adaptively produce the homogeneous regions to get the effective descriptors. Then, we adopt a similar idea in spectral part that reasonably aggregating the channels to generate spectral descriptors for spectral graph contexts capturing. All graph reasoning procedures in SAGRN and SEGRN are achieved through graph convolution. To guarantee the global perception ability of the proposed methods, all adjacent matrices in graph reasoning are obtained with the help of non-local self-attention mechanism. At last, by combining the extracted spatial and spectral graph contexts, we obtain the SSGRN to achieve a high accuracy classification. Extensive quantitative and qualitative experiments on three public HSI benchmarks demonstrate the competitiveness of the proposed methods compared with other state-of-the-art approaches.