In　this　paper,　we　study　the　Cauchy　problem　of　density-dependent　Boussinesq　equations　for　magnetohydrodynamics　convection　on　the　whole　2D　space.　We　first　establish　global　and　unique　strong　solution　for　the　2D　Cauchy　problem　when　the　initial　density　includes　vacuum　state.　Furthermore,　we　consider　that　the　initial　data　can　be　arbitrarily　large.　We　derive　a　consistent　priori　estimate　by　the　energy　method,　and　extend　the　local　strong　solutions　to　the　global　strong　solutions.　Finally,　we　obtain　the　large-time　decay　rates　of　the　gradients　of　velocity,　temperature　field,　magnetic　field　and　pressure.