To enhance the inferior energy-absorption performance of a hydraulic support during coal mine rock burst, which leads to failure and damage, a framework including a kind of corrugated laminated energy-absorbing component on the top beam of the hydraulic support is developed. First, triangular, trapezoidal and sinusoidal corrugated core energy-absorbing structures are designed, and their mathematical models are established. Second, three kinds of corrugated core components are optimized to obtain the suitable structural parameters, and based on the findings, the energy-absorption characteristic curves of the three kinds of corrugated core components are obtained through a simulation analysis. The results show that the sinusoidal corrugated core exhibits the best energy-absorption effect among the single-layer corrugated components. Among the two-layer and four-layer corrugated core components, the triangular corrugated core arrangement is the optimal arrangement. The energy absorption of the three kinds of corrugated core components is correlated with the delamination. The results of the experiment and simulation are consistent. This study provides a theoretical basis and experimental reference for the design of energy-absorbing components for an anti-impact hydraulic support.