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Inspired by that high resolution patches,which is the sparse linear combining of the over complete dictionary,can well match the low resolution patches. A new super resolution algorithm based on regression function and local self-similarity is proposed. Compared with the general single-frame super resolution algorithm,the advantage of the proposed algorithm combines the learning of example patches and local self-similarity. Local regression of example patches can avoid the ill-posed problem of LR patches to HR patches. Another aspect,the first-order approximation of the nonlinear mapping function obtained by local self-similar example patches can get the pair of the LR patches corresponding to the HR patches. That overcomes the shortcomings of examples patch algorithms. In this paper,Peak Signal to Noise Ratio (PSNR) and Root-mean-square error (RMSE) is used to compare the results of the algorithms. The data results show that the proposed algorithm has the highest PSNR value and the lowest MSE value in most cases. The experimental graph results show that the image’s texture can be reserved best,the nature of the images is very good. And the execution time of proposed algorithm is less than several other algorithms,which indicates the proposed algorithm is more suitable for applying to settle practical issue.