Description: Compared with color or grayscale images, hyperspectral images deliver more informative representation of ground objects and enhance the performance of many recognition and classification applications. However, hyperspectral images are normally corrupted by various types of noises, which have a serious impact on the subsequent image processing tasks. In this paper, we propose a novel hyperspectral image denoising method based on tucker decomposition to model the nonlocal similarity across the spatial domain and global similarity along the spectral domain. In this method, 3-D full band patches extracted from a hyperspectral image are grouped to form a third-order tensor by utilizing the nonlocal similarity in a proper window size. In this way, the task of image denoising is transformed into a high-order tensor approximation problem, which can be solved by nonnegative tucker decomposition. Instead of a traditional alternative least square based tucker decomposition, we propose a hierarchical least square based nonnegative tucker decomposition method to reduce the computational cost and improve the denoising effect. In addition, an iterative denoising strategy is adopted to achieve better denoising outcome in practice. Experimental results on three datasets show that the proposed method outperforms several state-of-the-art methods and significantly enhances the quality of the corrupted hyperspectral image.