Band selection aims at selecting a subset of representative bands from original hyperspectral images (HSIs) to alleviate data redundancy. There are at least two issues existing in previous methods. First, most of them ignore global or local structural information without considering both two aspects. Second, the high-order correlations among spectral bands are not explored during learning. In this paper, we propose a tensorial global-local graph self-representation (TGSR) method for hyperspectral band selection. Specifically, we segment the HSI into diverse superpixels to show the inherent spectral-spatial structures. Based on the generated superpixels, we learn the global and local graphs to explore complex structural information from global pixels and local regions. To alleviate the computational burden, a transformation is designed for easy graph convolution of global graph and pixel spectral matrix. With global and local knowledge, we formulate a global-local graph self-representation model to conduct band correlation learning in a self-weighted manner. To explore the high-order correlations among bands, we reorganize the self-representation coefficient matrices into a tensor with low-rank constraint. We design an alternating optimization algorithm to solve the proposed model. The most representative band is selected from each band subset by performing spectral clustering on the constructed affinity matrix. Experiments on HSI datasets verify the effectiveness of our method over the state-of-the-art methods. The source code is released at https://github.com/ZhangYongshan/TGSR.