A single-layer and double-layer corrugated core sandwich structure consisting of carbon fibre–reinforced polymer (CFRP) panels and aluminium alloy core layers was designed. Numerical simulations were carried out in HyperMesh/LsDyna, and the simulation results of single-layer and double-layer corrugated sandwich structure were compared with the experimental results to verify the reliability of the proposed numerical model. Compared with the results of single-layer and double-layer corrugated sandwich structure, the superiority of a double-layer corrugated sandwich structure in anti-collision performance is verified. Considering the effects of impact energy and impact position on impact force, energy absorption capacity, and failure mode, a series of low-velocity impact finite element simulations was carried out. It was found that the main failure mode of composite laminates included fibre damage, matrix damage and delamination, and core buckling. At the same impact position, the higher the impact energy, the greater the initial slopes of the contact force-time and absorbed energy-time curves, the higher the peak force, and the larger the energy absorption capacity. Under the same impact energy, when the impactor hit the wave crest of the sandwich structure, the damage to the structure was small; however, the maximum impact force on the structure was large (∼8 kN).