Visually　meaningful　image　encryption　(VMIE)　means　that　a　plain　image　is　transformed　into　a　visually　meaningful　cipher　image　which　makes　the　plain　image　more　imperceptible　than　the　noise-like　cipher　image　generated　by　traditional　image　encryption　algorithms.　In　essence,　existing　VMIE　algorithms　exploit　the　idea　of　information　steganography,　i.e.,　embedding　a　secret　into　a　host　image　to　generate　a　cipher　image　which　is　visually　similar　to　the　original　host　image.　However,　it　is　well　known　that　steganalysis　technique　is　a　fatal　threat　to　steganography.　Therefore,　the　security　of　existing　VMIE　algorithms　will　be　potentially　threatened　by　steganalysis　technique.　To　improve　the　security　of　VMIE　algorithms,　we　propose　a　new　VMIE　framework　with　dual　embedding　model.　In　the　new　framework　an　additional　embedding　phase　is　added.　More　specifically,　in　the　first　embedding　process,　the　pre-encrypted　image　is　embedded　into　the　reference　image　to　generate　a　visually　meaningful　reference　cipher　image.　In　the　second　embedding　process,　the　difference　between　the　visually　meaningful　reference　cipher　image　and　the　original　reference　image　is　calculated　to　obtain　a　deviation　matrix.　Then,　the　deviation　matrix　is　used　as　the　disguised　information　and　then　embedded　into　the　disguised　host　image　to　obtain　a　disguised　visually　meaningful　encrypted　image.　The　reference　image　can　be　any　image　with　specified　size　thus　ensuring　the　security　of　the　VMIE　algorithm.　To　verify　the　validity　of　the　proposed　VMIE　framework,　an　example　algorithm　is　proposed.　Simulation　results　and　performance　analyses　show　that　the　example　algorithm　has　a　high　time　efficiency,　high　robustness　and　security.