This project proposes a new hyperspectral image (HSI) denoising method that is able to cope with additive mixed noise, i.e., mixture of Gaussian noise, impulse noise, and stripes, which usually corrupt hyperspectral images in the acquisition process. The proposed method fully exploits a compact and sparse HIS representation based on its low rank and self-similarity characteristics. In order to deal with mixed noise having a complex statistical distribution, we propose to use the robust data fidelity instead of using the  data fidelity, which is commonly employed for Gaussian noise removal. In a series of experiments with simulated and real datasets, the proposed method competes with state of the art methods, yielding better results for mixed noise removal. This project is implemented with MATLAB software.