Low-rank representation is one of the state-of-art hyperspectral image denoising algorithms, but it suffers from ignoring the high-order relations between data points in images. We propose a hypergraph Laplacian regularized low-rank representation algorithm for noise reduction of hyperspectral images, which can represent the high-order relations between data points by using the hypergraph Laplacian regularization. The ability of maintaining the local information is improved, and the sparse and non-negative constraints are added to the model coefficient matrix. The proposed method not only resumes the low-rank signal components, but also represents the high-order relations of the image data. Experimental results on AVIRIS and ProSpecTIR-VS images show that the proposed approach can maintain the spatial and spectral information of images better, which improves the denoising results of hyperspectral images effectively.