Crystal　phase　engineering　is　an　important　strategy　for　designing　noble-metal-based　catalysts　with　optimized　activity　and　stability.　From　the　thermodynamic　point　of　view,　it　remains　a　great　challenge　to　synthesize　unconventional　phases　of　noble　metals.　Here,　a　new　class　of　Pd-based　nanostructure　with　unconventional　rhombohedral　Pd20Sb7　phase　is　successfully　synthesized.　Benefiting　from　the　high　proportion　of　the　unique　exposed　Pd20Sb7　(003)　surface,　Pd20Sb7　rhombohedra　display　much　enhanced　ethanol　oxidation　reaction　(EOR)　and　oxygen　reduction　reaction　performance　compared　with　commercial　Pd/C.　Moreover,　Pd20Sb7　rhombohedra　are　also　demonstrated　as　an　effective　air　cathode　in　non-aqueous　Li-air　batteries　with　an　overpotential　of　only　0.24　V.　Density　functional　theory　calculations　reveal　that　the　unique　exposed　facets　of　Pd20Sb7　rhombohedra　can　not　only　reduce　the　excessive　adsorption　of　CH3CO*　to　CH3COOH　on　Pd　for　promoting　EOR　process,　but　also　weaken　CO　binding　and　CO　poisoning.　This　work　provides　a　new　class　of　unconventional　intermetallic　nanomaterials　with　enhanced　electrocatalytic　activity.