This paper proposes a new interpolation approach for obtaining high resolution (HR) images from its low resolution (LR) images. We are using the Least Squared based block by block prediction scheme to estimate the predictors using Jacobian iteration method. In spite of Jacobian's Iterative property of convergence for diagonally dominant matrices only, our proposed method uses this property effectively for all types of matrices, and found a set of prediction coefficients using a small number of iterative steps. Due to its lesser computational cost it can be used in real time applications too. Use of iterative methods like Jacobi gives an advantage of its application over images which gives singular matrices during operation. Experimental results indicates that the proposed algorithm gives better quantitative performance as compared to other conventional interpolation techniques. © 2012 IEEE.