Electromagnetic wave propagation in three-dimensional (3D) space typically suffers omnidirectional scattering when encountering obstacles. In this study, we used Chern vectors to construct a topological heterostructure, where large-volume nonreciprocal topological transport in 3D is achieved. The shape of the cross section in the heterostructure can be arbitrary designed, and we experimentally observed the distinctive cross-shaped field pattern transport, nonreciprocal energy harvesting, and the remarkable ability of electromagnetic wave to traverse obstacles and abrupt structure changes without encountering reflections in 3D space.