In order to reconstruct the original image from strong noise image and reduce the error, an improved image denoising algorithm for strong noise images is proposed, which is addressed as gradient reweighted non-local averaging. According to the sparse and redundant representation, the approach is based on K-SVD trained dictionaries, which are learned from the corrupted image itself and lead to sparser representations. Nevertheless, the denoising quality is bad for the strong noise image because of the intrinsic structure of dictionaries. The method is proposed to find the inherent structure of images using non-local averaging algorithm with gradient reweighting, which is obtained by total variation, as the tighter constraint over the image. According to the information of edges as the image prior and the redundancy, the optimized solution is used to solve an inverse problem by defining the area of edges higher weights. Compared with the traditional dictionary denoising, the proposed algorithm not only show the superiority of the noise drawn images in peak signal to noise ratio, but also keeps the detail information in structure similarity.