In this paper, we study homogeneous Einstein
0362546X16302255&_mathId=si1.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=561ee59c7a09ce05fabc91db207da099" title="Click to view the MathML source">(α,β)-metrics on compact Lie groups and spheres. We first show that any left invariant Einstein
0362546X16302255&_mathId=si1.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=561ee59c7a09ce05fabc91db207da099" title="Click to view the MathML source">(α,β)-metric on a connected compact simple Lie groups except
0362546X16302255&_mathId=si4.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=a52e27b0eb814cc3292942ddcb5ca75c">
0362546X16302255-si4.gif"> with vanishing S-curvature must be a Randers metric. Secondly, we prove that any
0362546X16302255&_mathId=si5.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=8c5dcab0fccc57c3880422a206572b28">
0362546X16302255-si5.gif">-invariant Einstein
0362546X16302255&_mathId=si1.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=561ee59c7a09ce05fabc91db207da099" title="Click to view the MathML source">(α,β)-metric on
0362546X16302255&_mathId=si7.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=65d7e30d4c8c6d1539830f07993f323b" title="Click to view the MathML source">S4n+3(n∈N+) with vanishing S-curvature is either a Randers metric, or
0362546X16302255&_mathId=si8.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=3c2cb8680abe935af97e37d3be05a739">
0362546X16302255-si8.gif">-invariant. Finally, we give a complete description of
0362546X16302255&_mathId=si9.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=f59eea0e254f465bd61eeaf569063b45">
0362546X16302255-si9.gif">-invariant Einstein Finsler metrics on
0362546X16302255&_mathId=si10.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=ae54773e1f38f8c55a8c8341c0cc4436" title="Click to view the MathML source">S2n+1(n≥2).