Dynamic crushing responses and energy absorption of functionally graded folded structures with foam fillers are investigated in this study. The proposed structure consists of multiple layers of folded truncated square pyramid (TSP) foldcore with foam fillers added inside each unit cells and the interlayer plates to separate each layer of foldcore and its foam filler. The foldcores are folded using pre-patterned thin aluminium sheets. Two types of foam including cubic shape expanded polystyrene (EPS) foam fillers with density of 13.5, 19 and 28 kg/m3 and rigid polyurethane (PU) foam of 35 kg/m3 with two shapes. Two sets of functionally graded multi-layer structures are achieved by varying the densities of EPS foam fillers (positively/negatively graded EPS) and varying the shapes of PU foam fillers (positively/negatively graded PU) inside each layer of TSP foldcore. These specimens are then crushed under 1 and 10 m/s. Under 1 m/s crushing, excellent crushing responses as energy absorber are observed for both negatively graded and positively graded multi-layer structures with low initial peak force and low fluctuation in resistance throughout deformation. Under 10 m/s crushing, however, positively graded structures show much more uniform load-displacement response with significantly reduced peak crushing force, increased energy absorption than negatively graded structures. Up to 60% increase in specific energy absorption is shown for folded structure with positively graded PU foam as comparing to the uniform structure without foam filler under 10 m/s crushing.