Traditional single core sandwich structures consist of two face sheets and one core. With an additional sheet, called internal sheet in this paper, inserted into the core, a two-core sandwich structure was then formed. Two-core sandwich structures with glass fiber/epoxy composite laminated face sheets and a thin internal sheet subjected to low velocity impact were studied, and attention was focused on the contact force responses of the two-core sandwich structures and effects of the locations of the internal sheet and levels of impact energy on the responses of the sandwich structures. A drop test was carried out and the contact force history between the projectile and the sandwich structures was then obtained. The results show that the contact force history of the two-core sandwich structures are affected significantly by the internal face sheet involved and the location of the internal face sheet.