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Block discrete cosine transform coding has been widely used in image and video compression standards. However, at low bit rate coding, the compressed image produces obvious block effects at the block boundaries, which seriously affect the image visualization. This paper combines Gaussian curvature regularization and structural sparse representation to remove the block artifacts appearing in the compressed images, while preserving sharp edges. More precisely, we use the internal structural sparse prior to remove the image noise, and apply the external structural sparse prior to prevent image overfitting. Meanwhile, we perform Gaussian curvature regularization constraint that blends image gradient information, in order to remove the detrimental structure of the compressed image. Concretely, we incorporate filtering technique into the alternating iteration method for handling the nonconvexity problem of the proposed model. Experimental results demonstrate that our algorithm achieves several state-of-the-art deblocking algorithms in terms of both objective and visual perception.