<p>The geometric design methods of energy-absorbing structures usually depend on the empirical combinations of basic geometric configurations, which lead to the poor universality, the low accuracy in discretization analysis for non-regular structures, and the insufficient stability in structural deformation. In this paper, a novel morphological function path-mapping design method for constructing irregular zero-Poisson’s ratio structures (NDPF) is proposed. The key is to characterize the center-symmetric configuration of the structure based on the predefined mathematical constraints. This approach can accurately calculate the structural displacements, enhance the deformation stability, and significantly improve the energy-absorbing properties of the structure. Specifically, the bending moment expression and the displacement of the structure are precisely derived. An analytical expression for the equivalent Poisson’s ratio of the structure is provided. The “breathing” stress transfer path of the NDPF is responsible for its high energy absorption performance. Hence, the stress concentration is transformed into a beneficial element in the structural design. The energy absorption performance of the NDPF is 1.34 times that of concave honeycomb structures and 2.75 times that of other non-regular structures with the same relative density, which shows the significant advantages of the morphological function path-mapping design method.</p>