In order to enhance image resolution and overcome the physical limitations of imaging systems, image super-resolution (SR) is proposed. In SR technique, a high resolution (HR) image is produced by fusing a sequence of low-resolution (LR) images.Since many recent approaches seeking an SR algorithm suppresses noise whilepreserving edges, in this paper, based-upon the statistical techniques, we have proposed an adaptive algorithmwhich is robust in the presenceof Gaussian noise -which has a high detrimental effect on image quality- and moreover, shows a good performance comparing to the other existing methods.In this adaptive algorithm we introducea set of weighting coefficients, which control the contribution between the dataerror and regularization terms in each of the estimated HR pixels. These coefficients are determined according to the neighbors information of the estimated pixel. Experimental results from both synthetic and real images confirm that theproposed algorithm outperforms the other methods.