In this study, we used HyperMesh and LS-DYNA software, based on the MAT54 model and Chang-Chang failure criterion, to establish a finite element model of composite corrugated sandwich structures, and introduced a progressive damage model. The impact resistance of the corrugated sandwich structure was studied by analysing the residual velocity of the projectile, the impact force of the target plate, and the failure mode. The impact resistance of the corrugated sandwich structure was analysed when four types of composite materials were used as the front and back panels of the corrugated sandwich structure. The results showed that, compared with the metal aluminium panel, the impact resistance of the structure was high when ultra-high molecular weight polyethylene (UHMWPE) fibres were used as the positive panel. When the composites were used as the back panel, although the residual velocity was lower than metal aluminium, the impact force was higher than metal aluminium, with more serious damage form of the target plate. Thus, the impact resistance of composite front panel/metal aluminium core/metal aluminium back panel sandwich structure was better than the all-metal aluminium corrugated sandwich structures. The results of this paper can provide a reference for the design of novel lightweight multifunctional structures.