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Chiral hyper-structure is a family of lightweight structure with negative Poisson's ratio, which leads benefit in mechanical properties and designability. In order to further improve some mechanical properties of chiral hyperstructures, the concept of gradient is introduced into the structure. Five groups of gradient tetra-chiral hyper-structure with different gradient factors are fabricated based on waterjet cutting technology, and the in-plane quasistatic lateral compression tests are carried out. Finite element models are developed for the in-plane linear elastic mechanical properties and plastic deformation modes under lateral compression condition. Theoretical prediction models of elastic modulus in gradient direction and Poisson's ratio of the gradient tetra-chiral hyper-structure is derived based on geometric assumptions and inhomogeneous deformation mode which are verified by experiments and finite element analysis. Simultaneously, the effects of gradient factors on the deformation characteristics and mechanical behaviors of the tetra-chiral hyper-structure are discussed and analyzed.