This paper presents a novel spectral-spatial destriping method for hyperspectral images, based on spectral sparse representation and unidirectional huber-markov random field. Research on the hyperspectral image analysis suggests that destriping is an ill-posed inverse problem essentially. To alleviate this problem, three spectral and spatial prior constraints are modeled in this work. Firstly, the spectral sparsity prior is modeled to measure the relation between the subimages in distinct bands of the given hyperspectral image. Then the spatial reconstruction constraint is used to encourage the restored result to be consistent with the useful information in the noisy subimage. Since the striping noise is unidirectional in general, a spatial unidirection prior is proposed to reduce stripes while alleviating the problem of over smoothing. Finally, the priors above are integrated into a unified convex objective function, which can be efficiently solved by the augmented Lagrange method. The experimental results on two real hyperspectral datasets validate the efficacy of the proposed method for hyperspectral image destriping.