In this paper, a novel video super-resolution image reconstruction algorithm is proposed. We design a patch-based low rank matrix completion algorithm. The proposed algorithm addresses the problem of generating a high-resolution (HR) image from several low-resolution (LR) images, based on sparse representation and low-rank matrix completion. The approach represents observed LR frames in the form of sparse matrices and rearranges those frames into low dimensional constructions. Experimental results demonstrate that, high-frequency details in the super resolved images are recovered from the LR frames. The gains in terms of PSNR and SSIM are significant.