In　this　paper,　we　are　devoted　to　study　the　Cauchy　problem　of　the　incompressible　density-dependent　Boussinesq　equations　of　Korteweg　type　with　vacuum.　We　establish　some　key　spatial　weighted　estimates　and　a　priori　decay-in-time　rate　of　the　strong　solutions　by　using　the　energy　method.　Furthermore,　we　prove　that　there　is　a　unique　global　strong　solution　for　the　2D　Cauchy　problem　when　the　spatial　weighted　norm　of　the　initial　density　is　suitably　small.　Finally,　we　also　obtain　the　large　time　decay　rates　for　the　gradients　of　velocity,　temperature　and　pressure.(c)　2022　Elsevier　Ltd.　All　rights　reserved.