In　this　paper,　we　study　the　Cauchy　problem　of　the　incompressible　Bénard　system　with　density-dependent　viscosity　on　the　whole　three-dimensional　space.　We　first　construct　a　key　priori　exponential　estimates　by　the　energy　method,　and　then　we　prove　that　there　is　a　unique　global　strong　solution　for　the　3D　Cauchy　problem　under　the　assumption　that　initial　energy　is　suitably　small.　In　particular,　it　is　not　required　to　be　smallness　condition　for　the　initial　density　which　contains　vacuum　and　even　has　compact　support.　Finally,　we　obtain　the　exponential　decay　rates　for　the　gradients　of　velocity,　temperature　field　and　pressure.　©　2023　International　Press.