This paper presents a novel destriping method for hyperspectral images. Most of the previous destriping methods regard only the corrupted subimage as an isolated image and fail to consider the high spectral correlation between the subimages in different bands. This may impede their performance of removing striping noises. The proposed method takes advantage of both spectral and spatial information to contribute to the process of striping noise reduction. Firstly, a correntropy-based sparse representation (CSR) model is utilized to learn the high spectral correlation between the subimages in different bands. Then the spatial information of the target subimage with striping noise is incorporated into the CSR model with a unidirectional Huber-Markov random field prior. We devise an Augmented Lagrange Multiplier type of algorithm to efficiently compute the destriped results. The experimental results on two real-world hyperspectral data sets demonstrate the effectiveness of the proposed method.