In　this　paper,　we　study　the　existence　and　uniqueness　of　positive　solutions　for　a　class　of　higher-order　nonlocal　fractional　differential　equations　with　Riemann-Stieltjes　integral　boundary　conditions.　We　firstly　convert　the　problem　to　an　equivalent　integral　equation,　and　then　by　applying　a　fixed　point　theorem　of　a　sum　operator,　the　existence　and　uniqueness　of　positive　solutions　is　established.　Furthermore,　an　iterative　scheme　to　approximate　the　solution　is　constructed　and　an　example　is　given　to　illuminate　the　application　of　the　main　results.