Negative Poisson’s ratio（NPR） structure has been widely used in aerospace, biomedicine and military equipment and other fields owing to its outstanding energy absorption and adjustable volume. A novel type of inclined cross-like cellular re-entrant structure with negative Poisson’s ratio in horizontal and vertical directions and positive Poisson’s ratio in 45° oblique direction is proposed. The analytical expressions of the equivalent elastic modulus, equivalent Poisson’s ratio and relative density of the structure are derived by using the energy method and Castigliano’s second theorem. The correctness of the analytical expression is verified by finite element simulation and experimental test. Meanwhile, the effects of the geometric parameters on the equivalent elastic modulus and Poisson’s ratio are given. The research results improve the mechanical properties of this kind of structure, and provide a theoretical basis for its promotion and application in engineering practice.