This study examines the nonlinear dynamic response of sandwich plates under low-velocity impacts (LVIs), which consist of a porous aluminum foam core with functionally graded (FG) graphene platelets (GPLs) reinforcement and two titanium alloy face sheets. The finite element method is employed to perform the numerical simulations and the Hertz contact theory is used to model the impact behavior. The generic Halpin-Tsai model, which incorporates the porosity effect, is adopted to estimate the mechanical properties of core made of the FG-GPLRC, based on the experimental data of the closed-cell aluminum alloy foam. The simulation results reveal that the FG-X configuration has the highest impact resistance, and that the addition of GPLs improves the impact performance. Moreover, a thicker core can reduce both the first contact time and the vibration period of plates, while a looser boundary condition can prolong the vibration time after the first impact. Additionally, a higher impactor velocity, mass and radius lead to a higher deflection and contact force. The oblique impact decreases the impact energy. This work provides a lighter and stiffer design for structure engineers when components suffer low-velocity impact.