Although deep neural networks (DNNs) have been widely applied to hyperspectral image (HSI) denoising, most DNN-based HSI denoising methods are designed by stacking convolution layer, which can only model and reason local relations, and thus ignore the global contextual information. To address this issue, we propose a deep spatial-spectral global reasoning network to consider both the local and global information for HSI noise removal. Specifically, two novel modules are proposed to model and reason global relational information. The first one aims to model global spatial relations between pixels in feature maps, and the second one models the global relations across the channels. Compared to traditional convolution operations, the two proposed modules enable the network to extract representations from new dimensions. For the HSI denoising task, the two modules, as well as the densely connected structures, are embedded into the U-Net architecture. Thus, the new-designed global reasoning network can help tackle complex noise by exploiting multiple representations, e.g., hierarchical local feature, global spatial coherence, cross-channel correlation, and multi-scale abstract representation. Experiments on both synthetic and real HSI data demonstrate that our proposed network can obtain comparable or even better denoising results than other state-of-the-art methods.