Abstract: Auxetic honeycomb structures have attracted significant research attention due to their lightweight nature, high specific strength, and superior damping properties. Recent studies have shown that the symmetry-broken re-entrant honeycomb exhibits higher energy absorption capabilities and auxetic performance. However, traditional two-dimensional configurations face limitations regarding spatial application in three-dimensional environments, it is difficult to take into account the lightweight design of the structure and the multi-directional negative Poisson's ratio, and a comprehensive description of the elastic properties for such structures is currently lacking. To address these issues, a three-dimensional bidirectional orthogonal symmetry-broken re-entrant auxetic honeycomb is proposed. Based on the small deformation hypothesis, a theoretical model of this novel structure is established using the force method to systematically analyze the influence of geometric parameters on elastic properties. To facilitate the practical application of the derived theoretical model and meet specific mechanical requirements, an inverse design approach based on the Non-dominated Sorting Genetic Algorithm II is implemented. By specifying the target equivalent elastic modulus and Poisson's ratio within a defined range, and incorporating geometric constraints, the optimal combinations of geometric parameters required to achieve the target properties are identified. Compared with the traditional trial and error design or artificial neural network method with large computational cost, the proposed inverse design framework can effectively avoid the generation of parameters that do not meet the geometric compatibility, and significantly improve the design efficiency and reliability. Finally, the validity and accuracy of the proposed theoretical model and the inverse design method are verified through Finite Element Analysis and experimental tests.