Municipal manholes are widely used in road engineering. However, due to the great differences in stiffness and deformation between the manhole cover and asphalt pavement, pavement diseases are frequently occurred around the manhole cover and serious noises are generated from the loosening cover under repetitive vehicular loadings, which can greatly reduce the overall integrity of the pavement structure and the drivers’ comfort. In this study, inspired by the unique properties in high energy absorption and negative Poisson’s ratio of origami structures, a Miura origami core layer-based sandwich energy dissipation transition structure was proposed to mitigate the performance differences between the manhole cover and the pavement under vehicular loads. First of all, a crease design theory inspired by Miura origami was proposed. Then, a sandwich hollow cylindrical structure was developed for energy dissipation using the Miura origami core layer, and its three-dimensional finite element model was developed using the ANSYS framework. In addition, the performance of the sandwich hollow cylindrical structure under vehicular loading was investigated, and the differences in responses among the manhole cover, the proposed structure, and the pavement were compared. The results showed that the sandwich hollow cylindrical structure exhibited excellent energy dissipation performance, and the responses of the pavement around the manhole were significantly reduced after the installation of such structure, promising a useful solution to the frequent occurrence of pavement diseases around manhole covers.