In　order　to　improve　the　tribological　properties　of　epoxy　resin　(EP),　graphene　was　functionalized　by　an　amine-riched　polymer,　polyethyleneimine　(PEI)　and　then　fabricated　the　P-GP/EP　composites.　The　tribological　behavior　of　P-GP/EP　composites　was　investigated　by　wear　testing　machine　and　micro-scratch　tester　from　macroscales　and　microscales,　respectively.　Meanwhile,　the　tensile　strength　and　microhardness　were　also　measured,　and　the　fracture　toughness　of　the　composites　was　evaluated　through　micro　scratch.　The　results　showed　that　the　friction　and　wear　properties　of　P-GP/EP　composites　were　improved　both　in　macroscales　and　microscales,　and　the　results　of　wear　resistance　were　consistent　under　macro　and　micro　tests.　The　wear　rate　in　macroscale　and　volume　loss　in　microscale　were　76.76%　and　51.34%　lower　than　those　of　pure　EP,　respectively.　The　tensile　strength,　hardness　and　fracture　toughness　of　the　composites　were　also　improved　by　the　addition　of　P-GP.　The　fracture　toughness　of　epoxy　composites　could　be　accurately　evaluated　based　on　linear　elastic　fracture　mechanics　(LEFM).　©　2020,　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.