Abstract: Based on the topology optimization method, the functional element topology optimization method was proposed to design a metamaterial and a functional element's structure with arbitrary negative Poisson's ratio. For different initial topological substrate structures of the functional element, including the rectangular and triangular initial topological substrate structure, with the specified negative Poisson's ratio as the constraint condition, the compliance of functional element was maximized as the objective function, and the topology optimization model with arbitrary negative Poisson's ratio was established and solved. The functional element was extracted by the topology optimal results, and the functional elements were periodically distributed to form a negative Poisson's structure. Then, the finite element model of the optimized metamaterial structure was established, and the Poisson's ratio of the functional element was calculated by the formula. Finally, the static and dynamic characteristics of the metamaterials were calculated and analyzed. The results demonstrate that this negative Poisson's ratio effect metamaterial specimen has good bearing capacity and has better vibration reduction performance in the middle and low frequency range.