We present a novel local shape descriptor, named wavelet energy decomposition signature (WEDS) for robustly matching non-rigid 3D shapes with different resolutions. The local shape descriptors are generated by decomposing Dirichlet energy on the input triangular mesh. Our approach can be either applied directly or used as the input to other learning-based approaches. Experimental results show that the proposed WEDS achieves promising results on shape matching tasks in terms of incompatible shape structures.