Multispectral image denoising is a basic problem whose results affect subsequent processes such as target detection and classification. Numerous approaches have been proposed, but there are still many challenges, particularly in using prior knowledge of multispectral images, which is crucial for solving the ill-posed problem of noise removal. This paper considers both non-local self-similarity in space and global correlation in spectrum. We propose a novel low-rank Tucker decomposition model for removing the noise, in which sparse and graph Laplacian regularization terms are employed to encode this prior knowledge. It can jointly learn a sparse and low-rank representation while preserving the local geometrical structure between spectral bands, so as to better capture simultaneously the correlation in spatial and spectral directions. We adopt the alternating direction method of multipliers to solve the resulting problem. Experiments demonstrate that the proposed method outperforms the state-of-the-art, such as cube-based and tensor-based methods, both quantitatively and qualitatively.