This paper focuses on developing a Super-resolution (SR) Magnetic Resonance (MR) image restoration method using Structural Group Sparsity Recovery Model (SGSRM). However, reformation of the original image is critically viewed as an acute problem in image processing, since there is no unique elucidation. In the process of tomography and medical image computing, it is crucial to reconstruct an image for several imaging modalities like X-ray, Computed tomography (CT), Magnetic resonance imaging (MRI), Positron-emission tomography (PET), and Single-photon emission computed tomography (SPECT). The quality of the reformed image from an original one depends mostly on the limitation of the diverse techniques. The principal purpose of this research is to improve the resolution in the restoration process of MR images by using structural group sparsity recovery model. The restoration dependent approach presumes that low-resolution (LR) images are warped, blurred, distorted and decimated from the respective high resolution (HR) images. The HR image is obtained from an array of LR images. In order to simplify the images at subpixel level and the record-keeping parameters among LR images are complicated, so the reformation of the image based on a usual SR procedure gives insufficient scope for enhancing the image resolution under general circumstances. The prevailing idea for image recovery has many different scopes, and the drawbacks can be overcome by using the structural group sparsity recovery model. By using the foreseeable structured portion group under SGSRM, it offers the idea to pick out the group of the portion within a cluster section. The SGSRM technique provides a superior resolution image by overcoming the drawbacks. The paramount impetus of this paper is to devise an SGSRM technique which is robust to noise, while most other SR techniques failed to provide de-noising and super-resolution concurrently with an impressive image resolution.