Recently, an Expected Patch Log Likelihood (EPLL) method is presented for image denoising, which can well restore details of natural images. However, the EPLL is viewed as a local method, and seldom takes into account the relationship among patches. In this paper, a non-local EPLL algorithm using eigenvectors of the graph Laplacian of patches is proposed to fully exploit such relationship. In detail, the eigenvectors of the graph Laplacian are incorporated as basis functions to employ the geometrical structures of patches. Meanwhile, the residual error constraint is considered to deal with the noise corruption in the iterative procedure. Sequently, an eigenvector-based EPLL problem is presented under a set of residual error constraints, and the corresponding approximate solution is efficiently provided. Experiments show that the proposed algorithm can achieve a better performance than the traditional EPLL, and is comparable with some other state-of-art denoising methods.