In　order　to　improve　the　efficiency　and　security　of　image　compression-encryption　algorithms,　we　propose　a　double　image　compression-encryption　scheme　based　on　fractional　hyper-chaotic　system　and　DNA　approach.　Firstly,　two　images　are　processed　by　discrete　cosine　transform.　Secondly,　the　spectrums　of　the　two　images　are　sorted　by　Z-scan,　so　that　the　two　images　can　be　compressed　and　mixed　into　a　new　image.　Finally,　the　resulting　image　is　encrypted　by　using　DNA　coding.　Different　from　traditional　image　encryption　algorithms,　the　proposed　algorithm　provides　a　variety　of　DNA　coding　and　operation　modes.　Chaotic　sequences　are　used　to　control　the　coding　and　operation　mode　in　order　to　improve　the　complexity　of　the　encryption　process.　Fractional　order　and　initial　values　of　fractional　order　hyper-chaotic　system　are　used　as　the　key　of　the　proposed　algorithm,　which　greatly　expands　the　complexity　and　the　key　space　of　the　scheme.　In　the　proposed　scheme,　by　mixing　two　images　and　performing　a　compression-encryption　operation　on　them　simultaneously,　the　proposed　algorithm　can　improve　the　complexity　of　encrypted　images　while　providing　good　confusion.　Experimental　results　and　security　analysis　show　that　the　proposed　algorithm　can　effectively　resist　multiple　attacks.