The　relationship　is　studied　here　between　the　3D　incompressible　Brinkman-Forchheimer　problem　with　delay　and　its　generalized　steady　state.　First,　with　some　restrictive　condition　on　the　delay　term,　the　global　well-posedness　of　3D　Brinkman-Forchheimer　problem　and　its　steady　state　problem　are　obtained　by　compactness　method　and　Brouwer　fixed　point　method　respectively.　Then　the　global　L-p(2　＜=　p＜infinity)　decay　estimates　are　established　for　weak　solution　of　non-autonomous　Brinkman-Forchheimer　equations　with　delay　by　using　a　retarded　integral　inequality.　The　global　decay　estimates　can　be　proved　for　strong　solution　as　well.　Finally,　the　exponential　stability　property　is　investigated　for　weak　solution　of　the　3D　non-autonomous　Brinkman-Forchheimer　problem　by　a　direct　approach　and　also　for　the　autonomous　system　by　using　a　retarded　integral　inequality.　Furthermore,　the　Razumikhin　approach　is　utilized　to　achieve　the　asymptotic　stability　for　strong　solution　of　autonomous　system　under　a　relaxed　restriction.