In the field of image processing, image denoising is quite challenging. The development of graph signal theory provides a new perspective for us to solve this problem. In this study, the weight matrix and the Laplace matrix based on a graph signal method are studied, and they are used for the objective function of image denoising. These two matrices can well define the internal relationship between the observed image and the expected image. After proposing the denoising objective function, we give the optimal solution and an iterative fast solution algorithm. Experiments show that this method is superior to cutting-edge denoising methods such as BM3D and WNNM.