We propose a nonrigid registration method whose motion estimation is cast into a feature matching problem under the Log-Demons framework using Graph Wavelets. We investigate the Spectral Graph Wavelets (SGWs) to capture the shape features of the images. The SGWs are more adapted to learn the spatial and geometric organization of data with complex structures than the classical wavelets. Our experiments on T1 brain images and endomicroscopic images show that this method outperforms the existing nonrigid image registration techniques (i.e. Log-Demons and Spectral Log-Demons) with improved similarity values.