As a new type of smart materials and structures, the accurate prediction of the nonlinear mechanical properties of metamaterial structures with negative Poisson's ratio under large strains is of great significance for their potential applications in engineering. In this paper, a class of metamaterial structures enhanced by straight struts are designed by adding straight struts to ratio arc-shaped structures with negative Poisson's ratio. The analytical expressions of the transverse/longitudinal equivalent Poisson's ratio and equivalent elastic modulus of the concave honeycomb structure are derived by energy method. The effects of structural parameters on the equivalent Poisson's ratio and equivalent elastic modulus of the structure are discussed. Considering the geometric nonlinearity under large deformation, a finite element model of re-entrant arc-shape structure with negative Poisson's ratio is established. The correctness of the analytical expression is verified by comparing with the linear simulation results. The results show that the equivalent Poisson's ratio and equivalent elastic modulus both varies with the increase of deformation. The differences increase with the increased deformation. Therefore, geometric nonlinearity analysis must be considered in the case of large deformation. The vibration reduction performance of the designed metamaterial structure is calculated by using the harmonic response analysis. The analysis shows that the overall damping performance of the structure increases gradually with the increase of the number of layers. The overall vibration reduction performance of the structure does not change with the frequency, and the response to excitation can play a very good inhibitory effect in the low frequency range. Therefore, the rational design of metamaterial microstructure has a good effect on the low frequency vibration suppression of structures, and has a certain reference significance for the design of vibration reduction metamaterial with negative Poisson's ratio.