This　paper　is　concerned　with　the　long-time　dynamics　and　asymptotic　stability　for　the　3D　Brinkman-Forchheimer　equation　with　delay　on　some　unbounded　domains.　The　global　well-posedness　of　the　3D　BrinkmanForchheimer　flow　is　investigated　by　a　truncation　method　firstly,　then　the　pullback　attractor　has　been　presented　for　the　process　generated　by　weak　solutions.　Furthermore,　the　exponential　stability　between　evolutionary　and　stationary　solutions　has　been　shown　by　some　estimate　of　elliptic　equation.