Abstract: The traditional methods based on linear regression model preserve the edge in some degree, but hardly work on the sharp edge. To solve this problem, an edge directed interpolation algorithm based on regularization is proposed in this paper, which is composed of the parameters estimation part and the data estimation part. In the first part, the high resolution structures which have been estimated are taken as one part of the training pixel to estimate the parameters of the linear regression model for effectively describing the structure. In the second part, the smooth pixels direction is applied as the regularization to reduce the error of estimated data aroused from the incorrect parameters. Experimented results show that the proposed method preserves the edge of image effectively, and both the visual effects and the PSNR are all better than bi-cubic and Regularized Local Linear Regression (RLLR).