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In this paper, chiral metamaterials (CMM) were optimized from conceptual design to fine design with the effective elastic constants unchanged under finite strain. First, through calculation and comparison of examples, the unit cell method was selected to compute the effective elastic properties of the periodic chiral metamaterials under finite strain. Secondly, the conceptual design of chiral metamaterials with prescribed Poisson's ratios under finite strain was realized through density-based and feature-driven topology optimization. Then, the method of moving asymptotes (MMA) was used to solve the optimization problems. Based on the optimal configuration, chiral metamaterials with prescribed Poisson's ratios and Young's moduli under finite strain were carefully designed through shape optimization. Genetic algorithm was used to solve the optimization problem. Finally, the optimal models were fabricated by 3D printing. The optimal design was validated by tensile test results, i.e., the designed chiral metamaterials can maintain effective elastic properties under large deformation, and the invariance of the effective elastic properties depends on the nonlinearity of the flexible chiral metamaterials. [ABSTRACT FROM AUTHOR]