In this paper, we propose an edge directive moving least square (ED-MLS) based superresolution method for computational integral imaging reconstruction(CIIR). Due to the low resolution of the elemental images and the alignment error of the microlenses, it is not easy to obtain an accurate registration result in integral imaging, which makes it difficult to apply superresolution to the CIIR application. To overcome this problem, we propose the edge directive moving least square (ED-MLS) based superresolution method which utilizes the properties of the moving least square. The proposed ED-MLS based superresolution takes the direction of the edge into account in the moving least square reconstruction to deal with the abrupt brightness changes in the edge regions, and is less sensitive to the registration error. Furthermore, we propose a framework which shows how the data have to be collected for the superresolution problem in the CIIR application. Experimental results verify that the resolution of the elemental images is enhanced, and that a high resolution reconstructed 3-D image can be obtained with the proposed method.