Compared to traditional color or grayscale images, hyperspectral image (HSI) can help deliver more faithful representation of ground objects and enhance the performance of many computer vision tasks. However, an HSI is often corrupted by various noises, which has serious impact on the subsequent processing. Considering the non-local similarity across spatial domain and global similarity along spectral domain, a novel denoising method based on tensor decomposition is proposed in this paper. Firstly, 3D full band patches extracted from the HSI are grouped to form a 4th-order tensor by utilizing the non-local similarity in a proper window size. Then the task of hyperspectral image denoising is transformed into a high order tensor approximation problem, which can be efficiently solved by alternating optimization. An iterative denoising strategy is adopted for better effect in practice. Experimental results on simulated and real HSI data show that the proposed algorithm outperforms several state-of-the-art methods.