To address the problem of unsatisfy corresponding accuracy due to insufficient local deformation recognition in 3D shape correspondence, we proposed a shape corresponding method based on a region energy aware capsule network. First, the energy regions of the model are formed by merging the over-segmented patches of the 3D mesh based on the regional energy merging rules. Then, a region energy aware capsule network (REA-CapsNet) is designed to improve the accuracy of feature correspondence results. Moreover, the network model is optimized by the knowledge distillation strategy of energy migration to further improve the convergence speed of the network. Finally, the region energy constraint is embedded in the functional maps to obtain the function mapping matrix with high accuracy and robustness. On four datasets of FAUST, SCAPE, TOSCA and KIDS, the overall average geodesic error of REA-CapsNet reaches 0.075 7, 0.203 2, 0.081 8 and 0.134 2 respectively, indicating that the proposed method has great accuracy and generalization.