In this paper, we present a novel iterative interpolation super-resolution algorithm based on the edge-directed interpolation algorithm (NEDI) and the iterative-interpolation super-resolution algorithm (IISR). Our proposed algorithm introduces the NEDI which has only been used for single-image interpolation in previous researches into multi-frame interpolation area of the IISR by way of mapping two images with a 0.5 pixel shift along both directions into a high-resolution grid and populating the grid using improved NEDI. The novel algorithm employs an iterative interpolation process which can be divided into two steps. Firstly, we map low resolution images into the high resolution grid, and use the new interpolation method based on improved NEDI to interpolate the grid to create the first approximation image. Secondly, to satisfy the observation constraints provided by the given low-resolution images, we implement the iteration procedure during which the error vector between the simulated low resolution image and the original one is reconstructed into a high-resolution error image using the same interpolation technique as the first approximation image. After several iteration cycles, the reconstructed high resolution image converging to the real scene is achieved. Absorbing the merits of NEDI and the iterative procedure as well as the improvement to them, the proposed algorithm can preserve the edges well and achieve higher reconstruction accuracy without amplifying the noise and with very few artifacts though using insufficient low resolution images. At last, we carry out a simulation experiment with grayscale images and color images, and the new algorithm demonstrates much better performance compared with some previous normal methods, and the application to noise corrupted low resolution images confirms its robustness.