Denoising is an important preprocessing step to further analyze the hyperspectral image (HSI), and many denoising methods have been used for the denoising of the HSI data cube. However, the traditional denoising methods are sensitive to outliers and non-Gaussian noise. In this paper, by utilizing the underlying low-rank tensor property of the clean HSI data and the sparsity property of the outliers and non-Gaussian noise, we propose a new model based on the robust low-rank tensor recovery, which can preserve the global structure of HSI and simultaneously remove the outliers and different types of noise: Gaussian noise, impulse noise, dead lines, and so on. The proposed model can be solved by the inexact augmented Lagrangian method, and experiments on simulated and real hyperspectral images demonstrate that the proposed method is efficient for HSI denoising.