Denoising is an essential task in hyperspectral image preprocessing that can improve the performance of subsequent applications. We propose an iterative hyperspectral images denoising method that results in two algorithms, one global and one nonlocal. Both are based on a higher order singular value decomposition (HOSVD) sparse model and realize a regularization in each iteration. The proposed global algorithm treats the hyperspectral image as a whole entity that is able to jointly consider both spatial and spectral information and then uses an iterative regularization framework to mitigate the noise, while the nonlocal algorithm takes the advantages of a patch-based HOSVD sparse model and is more efficient. The experiments with both synthetic noisy and real hyperspectral images show that the proposed iterative method improves the hyperspectral image quality. The subsequent classification results further validate the effectiveness of the proposed hyperspectral image noise reduction.