Alternating　current　poling　(ACP)　is　an　effective　method　to　improve　the　piezoelectric　performance　of　relaxor-PbTiO3　(PT)　ferroelectric　single　crystal.　0.72　Pb(Mg1/3Nb2/3)O-3-0.28PbTiO(3)　(PMN-PT)　single　crystals　have　been　used　to　fabricate　piezoelectric　transducers　for　medical　imaging.　Up　to　date,　there　are　no　reports　about　the　full　matrix　material　constants　of　PMN-0.28PT　single　crystals　poled　by　ACP.　Here,　we　report　the　complete　sets　of　elastic,　dielectric,　and　piezoelectric　properties　of　[001]-poled　PMN-0.28PT　single　crystals　by　direct　current　poling　(DCP)　and　ACP　through　the　resonance　method.　The　results　show　that　[001]-poled　rhombohedral　PMN-0.28PT　single　crystals　exhibit　the　enhancement　of　longitudinal　and　transverse　piezoelectric　properties　(d(33)　similar　to　2000　pC/N,　d(31)　similar　to　-1010　pC/N)　after　ACP.　Compared　with　DCP　samples　(d(33)　similar　to　1660　pC/N,　d(31)　similar　to　-780　pC/N),　the　values　of　d(33)　and　d(31)　increase　20%　and　29%,　respectively.　While　the　dis　value　decrease　from　110　pC/N　for　DCP　sample　to　90　pC/N　for　ACP　sample,　showing　the　decrease　in　transverse　shear　piezoelectric　properties.　In　addition,　the　elastic　stiffness　coefficients　c(11),　c(12),　c(13),　the　elastic　compliance　coefficients　s(11),　s(12),　and　the　dielectric　constants　epsilon(1)(1),　epsilon(3)(3)　have　great　change　compared　with　DCP　and　ACP　samples.　This　variation　of　the　property　matrices　provides　a　reference　for　high-performance　piezoelectric　device　design.