In this paper, a sparse approximation algorithm using eigenvectors of the graph Laplacian is proposed for image denoising, in which the eigenvectors of the graph Laplacian of images are incorporated in the sparse model as basis functions. Here, an eigenvector-based sparse approximation problem is presented under a set of residual error constraints. The corresponding relaxed iterative solution is also provided to efficiently solve such problem in the framework of the double sparsity model. Experiments show that the proposed algorithm can achieve a better performance than some state-of-art denoising methods, especially measured with the SSIM index.