This study aimed to develop a mathematical design method for mechanical metamaterials considering the finite strain. Macrostructural properties for the finite deformation problem were estimated by extending the proposal by Zhang et al., which is a relatively simple and efficient way to estimate homogenization properties and calculate design sensitivity compared to homogenization theory. To design an ousetic mechanical metamaterial with negative Poisson’s ratio (NPR), the optimal design problem was formulated for obtaining a negative value of the effective Poisson’s ratio based on finite strain. The optimal structure geometry and topology of the representative volume elements (RVE), which were assumed to be periodically arranged, were obtained by a explicit level-set based topology optimization algorithm, previously proposed by some of the authors. There, to avoid the problem of numerical instability in finite deformation analysis (i.e., mesh collapses causing the optimization calculation to stop), a explicit structural presence/absence representation based on level-set and adaptive mesh methods was performed, and the structural exploring was driven by the reaction-diffusion equation. Through numerical examples, the optimal design solutions of RVE with NPR based on infinitesimal and finite strain energy were compared, and the validity of the proposed method was discussed.