Abstract:  At present，hyperspectral image has attracted more and more attention because of its rich spectral and spatial information that can recognize the ground objects.But because the hyperspectral image is very easy to produce Gauss，salt，pepper and stripe noise in the process of collection，has effect on subsequent spatial identification.Therefore，effective noise removal is an indispensable step in the hyperspectral image processing.Robust principal component analysis(RPCA) is a model which can more effectively recover the low rank matrix from sparse noise interference.Because of the high correlation between spectral features of hyperspectral images，the hyperspectral image itself has a very low rank.The RPCA model used to denoise the original hybrid photographic image with noise has raised more and more attention.The relevant RPCA algorithm used in the hyperspectral image denoising has achieved outstanding results.A new hyperspectral image denoising algorithm is proposed，which combines the neighborhood similarity of hyperspectral spatial feature and improved RPCA.Firstly，the low rank property of spectral information accords with the RPCA model assumption.Considering the Gaussian noise，the constraint term added to the Gauss noise is based on RPCA，which can more effectively eliminate the mixed noise.Then，we add the spatial similarity of the pixels of the hyperspectral image，that is，the similarity between the pixels and the pixels in the N neighborhood are added to the improved robust principal component analysis model.After that，the model is conductive to recover and rebuild the impaired spatial information and can retain more spatial detailed information of hyperspectral image.Whether the subjective vision or the objective evaluation index，the experiments show that the proposed algorithm has achieved significant improvement compared with the mainstream low rank model algorithm.