To　study　the　exisence　and　uniqueness　of　stutions　for　the　fractional　differential　equation　boundary　value　problem.　The　existence　and　uniqueness　of　positive　solutions　for　a　class　of　multi-point　fractional　differential　equation　boundary　value　problem　were　obtained　by　means　of　fixed　point　theorem　of　a　sum　operator　and　the　properties　of　Green　function.　An　iterative　scheme　to　approximate　the　solution　was　constructed　and　an　estimation　of　the　positive　solution　were　also　established.　An　application　was　given　as　an　example.　©,　2015,　Beijing　University　of　Technology.　All　right　reserved.