Demand　responsive　transit　(DRT)　is　emerging　as　one　of　the　most　potential　travel　modes　to　satisfy　flexible　travel　demands.　Nevertheless,　how　to　attract　more　passengers　has　become　a　critical　problem　in　the　success　of　DRT　projects.　It　is　necessary　to　take　into　account　the　psychological　factors　impacting　passengers＇　choices.　The　study　proposes　a　slack　departure　strategy　considering　boundedly　rational　passengers,　which　introduces　passengers＇　decision-making　psychology　into　the　optimization　process.　The　strategy　can　adjust　the　departure　time　of　passengers　to　adjacent　time　windows.　The　discount-incentive　mechanism　is　presented　to　attract　passengers　to　accept　the　changes　while　maintaining　the　quality　of　service.　On　this　basis,　the　theory　of　bounded　rationality　is　applied　to　describe　the　decision-making　process　of　passengers.　We　construct　a　multiobjective　programming　model　to　analyze　the　operator-passenger　interactive　effect.　To　address　the　multiobjective　problem,　a　two-phase　heuristic　algorithm　is　established　to　get　the　Pareto　solution　for　the　model.　A　numerical　experiment　is　carried　out　on　the　Sioux　Falls　network.　The　case　study　of　Beijing　is　discussed　to　evaluate　the　effectiveness　of　the　strategy.　The　results　indicate　that　the　slack　departure　strategy　can　significantly　benefit　both　the　operators　and　passengers.　The　operating　profit　substantially　increases　by　up　to　63%.　Meanwhile,　the　passenger＇s　general　travel　cost　declines　by　12%.　The　optimal　discount　rate　of　the　incentive　mechanism　is　20%.　Therefore,　the　study　contributes　to　comprehending　the　passenger＇s　decision-making　psychology　and　providing　a　new　optimization　strategy　for　the　operator　of　DRT.