An　image　compression-encryption　scheme　is　proposed　based　on　fractional　order　hyper-chaotic　systems　combined　with　2D　compressed　sensing　(CS)　and　DNA　encoding.　This　scheme　adopts　the　CS　technique　to　cut　down　the　size　of　the　original　image　proportionally　in　the　encryption　process　and　the　construction　parameters　of　the　CS　measurement　matrix　are　controlled　by　fractional　order　hyper-chaotic　systems.　The　chaotic　sequences　generated　by　fractional　order　hyper-chaotic　systems　are　used　to　dynamically　control　DNA　encoding　and　DNA　operation　mode　to　improve　the　complexity　of　encryption　process.　The　fractional　order　and　initial　value　of　the　fractional　hyper-chaotic　system　are　used　as　the　key　of　the　encryption　scheme,　which　greatly　expands　the　key　space　of　the　proposed　scheme.　The　proposed　scheme　maximizes　the　utilization　of　chaotic　sequences　generated　by　fractional　order　hyper-chaotic　systems,　and　the　chaotic　sequences　fit　perfectly　with　the　whole　process　of　the　scheme.　The　experimental　results　and　security　analysis　show　the　security　of　the　scheme　against　multiple　attacks.