With　wider　luminance　range　than　conventional　low　dynamic　range　(LDR)　images,　high　dynamic　range　(HDR)　images　are　more　consistent　with　human　visual　system　(HVS).　Recently,　JPEG　committee　releases　a　new　HDR　image　compression　standard　JPEG　XT.　It　decomposes　an　input　HDR　image　into　base　layer　and　extension　layer.　The　base　layer　code　stream　provides　JPEG　(ISO/IEC　10918)　backward　compatibility,　while　the　extension　layer　code　stream　helps　to　reconstruct　the　original　HDR　image.　However,　this　method　does　not　make　full　use　of　HVS,　causing　waste　of　bits　on　imperceptible　regions　to　human　eyes.　In　this　paper,　a　visual　saliency-based　HDR　image　compression　scheme　is　proposed.　The　saliency　map　of　tone　mapped　HDR　image　is　first　extracted,　then　it　is　used　to　guide　the　encoding　of　extension　layer.　The　compression　quality　is　adaptive　to　the　saliency　of　the　coding　region　of　the　image.　Extensive　experimental　results　show　that　our　method　outperforms　JPEG　XT　profile　A,　B,　C　and　other　state-of-the-art　methods.　Moreover,　our　proposed　method　offers　the　JPEG　compatibility　at　the　same　time.　©　2020　The　Author(s)　published　by　Cambridge　University　Press　in　association　with　Asia　Pacific　Signal　and　Information　Processing　Association.