Hyperspectral imaging has been widely applied in many fields due to the advantage of high spectral resolution. However, consisting of acquisition, transmission, reception and display, a hyperspectral imaging system may be disturbed in each part and thus leads to degradations that limit the precision of subsequent processing. It is therefore an important preprocessing step to remove the noise of acquired image data as much as possible. In this paper, we propose a novel regularization method for hyperspectral image denoising. Firstly, the low-rank and sparsity constraints are jointly used to establish the regularization model. For each spectral band, the low-rank constraint is for exploiting inter-column/- row correlations, while the sparsity constraint aims to exploit intra-column correlations. Secondly, reweighed ℓ1 norm strategy, which solves a sequence of weighted norm optimization problems and updates the weights with the solution ℓ1 of the last iteration, is introduced to approximate norm to achieve improved priori performance of the two ℓ0 constraints. Lastly, we apply the alternating direction method (ADM) under the augmented Lagrangian multiplier (ALM) framework to solve the model efficiently. Both low-rank and sparsity priors are reweighted at each iteration to promote low-rankness and sparseness of the solution. The denoising effect of our method is tested on real hyperspectral image data with different noise level. The experiments demonstrate the practicality of our proposed method.