Deformable non-rigid 3D shape retrieval plays an important role in various applications. Although there are many related works, their precision and robustness are not ideal. In this paper, we develop a novel retrieval method by using graph contexts, which consists of three steps. Initially, we evaluate the performance of spectral distances for deformable shape representation, which has not been studied in detail before. Then, we create a weighted L2distance for similarity measurement based on the spectra of Laplace-Beltrami operator. Finally, a new local graph diffusion method is introduced to reduce the mismatch error in feature space and the time cost of diffusion has reduced a lot simultaneously. Our experiment results on SHREC'11 Non-rigid dataset have reached the best reported retrieval performance (MAP: 99.9%).