This study aims to investigate the impact response and damage mechanism of cosine-function cell-based (CFCB) lattice core sandwich panels. Several low-velocity impact tests were conducted to explore their advantages in impact resistance by comparing them with traditional body-centered cubic (BCC) lattice-core sandwich panels. The impact response and deformation patterns of CFCB lattice core sandwich panels with two different faceplate materials (aluminum alloy and carbon fiber reinforced plastic composite) were experimentally investigated. The CFCB lattice core sandwich panels exhibited higher impact resistance and energy absorption capacity than their BCC lattice core counterparts. Furthermore, sandwich panels with aluminum alloy faceplates provided better impact resistance capacity than those with CFRP faceplates. Subsequently, several numerical models were developed to explore the deformation mechanisms and energy absorption characteristics of CFCB lattice core sandwich panels. In addition, the effects of the core structural parameters on mechanical performance were numerically investigated. Results indicated that increasing the cell rod diameter and/or reducing the cosine period length could decrease the indentation depth and enhance crush force efficiency. Finally, based on the principle of minimum potential energy, a theoretical model was developed to predict the initial peak load of CFCB lattice core sandwich panels with isotropic faceplates. This study aimed to explore the impact response and provide design guidance for CFCB lattice core sandwich panels.