The application of fiber-reinforced plastic (FRP) composite materials instead of metals, due to the low density of FRP materials, results in weight savings in the base plates of aircraft pallets. Lower weight leads to lower fuel consumption of the aircraft and thereby less environmental damage. The study aimed to investigate replacing the currently used aluminum base plates of aircraft pallets with composite sandwich plates to reduce the weight of the pallets, thereby the weight of the unit loads transported by aircraft. The newly constructed sandwich base plate consists of an aluminum honeycomb core and FRP composite face-sheets. First, we made experimental tests and numerical calculations for the investigated FRP sandwich panel to validate the applicability of the calculation method. Next, the mechanical properties of 40 different layer-combinations of 4 different FRP face-sheet materials (phenolic woven glass fiber; epoxy woven glass fiber; epoxy woven carbon fiber; and hybrid layers) were investigated using the Digimat-HC modeling program in order to find the appropriate face-sheet construction. Face-sheets were built up in 1, 2, 4, 6 or 8 layers with sets of fiber orientations including cross-ply (0°, 90°) and/or angle-ply (±45°). The weight optimization method was elaborated considering 9 design constraints: stiffness, deflection, skin stress, core shear stress, facing stress, overall buckling, shear crimping, skin wrinkling, and intracell buckling. A case study for the base plate of an aircraft pallet was introduced to validate the optimization procedure carried out using the Matlab (Interior Point Algorithm) and Excel Solver (Generalized Reduced Gradient Nonlinear Algorithm) programs. In the case study, the weight of the optimal structure (epoxy woven carbon fiber face-sheets) was 27 kg, which provides weight savings of 66% compared to the standard aluminum pallet. The article’s main added value is the elaboration and implementation of an optimization method that results in significant weight savings and thus lower fuel consumption of aircraft.