Three　mitigation　mechanisms　can　be　considered　in　the　design　of　an　impact　buffering　structure　made　of　granular　materials.　First,　reflection　and　decomposition　of　stress　wave　may　occur　at　the　interface　of　two　granules　of　different　materials.　Second,　energy　dissipation　happens　at　the　viscoelastic　contact　region　of　two　adjacent　granules.　Third,　the　impact　energy　carried　by　stress　waves　has　multiple　propagation　paths　in　two-　or　three-dimensional　granular　materials.　In　this　study,　a　two-dimensional　square　composite　structure　of　spherical　granules　(SCSPG)　employing　all　the　three　mitigation　mechanisms　is　designed　and　optimized　as　an　impact　buffering　structure.　A　numerical　model　is　established　to　investigate　the　propagation　behavior　of　impact-induced　stress　wave　in　a　SCSPG　composed　of　viscoelastic　spheres.　Comprehensive　evaluation　functions　are　established　to　evaluate　the　impact　mitigation　performance　of　the　SCSPG　based　on　the　consideration　that　the　probability　of　impact　varies　with　impact　location.　To　reduce　the　computational　complexity　in　the　material　optimization　process,　a　two-step　strategy　integrating　a　neural　network　with　a　genetic　algorithm　is　proposed.　The　hyperparameters　of　the　neural　network　are　optimized　for　the　purpose　of　achieving　high　accuracy　with　the　meta-data　generated　by　solving　the　numerical　model.　A　selection　criterion　of　an　optimal　material　combination　is　established　with　the　distribution　histogram　of　fitness　function＇s　values.　After　the　optimization,　the　numerical　solutions　of　stress　waves　in　SCSPG　are　improved,　thus　verifying　the　optimization　results　obtained　by　the　two-step　strategy.　After　the　optimization,　the　reduction　ratios　of　the　values　of　the　contact　force-dependent　and　the　velocity-dependent　functions　exceeded　55%　and　53%,　respectively.　The　proposed　evaluation　functions　and　the　developed　optimization　algorithm　are　applicable　to　the　design　of　high-performance　impact　mitigation　SCSPG.