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Hyperspectral image (HSI) denoising plays an important role in image quality improvement and related applications. Convolutional neural network (CNN)-based image denoising methods have been predominant due to advances made in the field of deep learning in recent years. Spatial and spectral information are crucial to HIS denoising, along with their correlations. However, existing methods fail to consider the global dependence and correlation between spatial and spectral information. Accordingly, in this article, we propose a novel dual-attention denoising network to overcome these limitations. We design two parallel branches to process the spatial and spectral information separately. The position attention module is applied to the spatial branch to formulate the interdependencies on the feature map, while the channel attention module is applied to the spectral branch to simulate the spectral correlation before the two branches are combined. A multiscale structure is also employed to extract and fuse the multiscale features following the fusion of spatial and spectral information. Experimental results on simulated and real data substantiate the superiority of our method both visually and quantitatively when compared with state-of-the-art methods.