A skin structure for thermal protection is one of the most interesting components that needs to be considered in the design of a hypersonic vehicle. The thermal protection structure, if a dense structure is used, is heavy and has a large heat conduction path. Thus, a lightweight, high strength structure is preferable. Currently, for designing a lightweight structure with high strength, natural materials are of great interest for achieving low density, high strength, and toughness. This paper presents bio-inspired lightweight structures that ensure high strength for a thermal protection system (TPS). A sinusoidal shape inspired by the microstructure of the dactyl club of Odontodactylus scyllarus, known as the peacock mantis shrimp, is presented with two different geometries, a unidirectionally corrugated core sandwich structure (UCS) and a bidirectionally corrugated core sandwich structure (BCS). Thermomechanical analysis of the two corrugated core structures is performed under simulated aerodynamic heating, and the total deflection and thermal stress are presented. The maximum deflection of the present sandwich structure throughout a mission flight was 1.74 mm for the UCS and 2.04 mm for the BCS. Compared with the dense structure used for the skin structure of the TPS, the bio-inspired corrugated core sandwich structures achieved about a 65% weight reduction, while the deflections still satisfied the limits for delaying the hypersonic boundary layer transition. Moreover, we first fabricated the BCS to test the thermomechanical behaviors under a thermal load. Finally, we examined the influence of the core thickness, face-sheet thickness, and emittance in the simulation model to identify appropriate structural parameters in the TPS optimization. The present corrugated core sandwich structures could be employed as a skin structure for metallic TPS panels instead of the honeycomb sandwich structure.