An apparatus for activating a pedestrian detection and collision mitigation system (PDCMS) of a vehicle , comprising: an engine management system , "EMS", acquiring speed information of the vehicle in real-time; an image collecting unit recognizing a pedestrian positioned within a driving lane of the vehicle and detecting information of a relative speed or a distance between the pedestrian and the vehicle , when a speed of the vehicle is greater than or equal to a set speed; and an electronic control unit , "ECU", activating a PDCMS function based on a mapping table using the speed information of the vehicle and information of a motion or a distance of the pedestrian with respect to the vehicle , and controlling a warning unit to inform a driver of a collision of the pedestrian with the vehicle , wherein the PDCMS function includes activating an operation of an active hood, activating an operation of the warning unit , and activating an operation of a brake regardless of whether the driver operates the brake, and the activation of the operation of the warning unit and the activation of the operation of the brake comprise, in order: activating the operation of the warning unit , activating a partial braking of the vehicle , and activating a full braking of the vehicle , wherein the electronic control unit is further configured to determine that the PDCMS function is operated, if an absolute value of the initial speed of the pedestrian at the boundary of a driving lane on which the pedestrian is moving is in a first speed range and the initial speed of the vehicle is in a second speed range at the time of determining whether the PDCMS function is operated, wherein the first speed range has a first minimum speed value and a first maximum speed value, and wherein the second speed range has a second minimum speed value and a second maximum speed value. an engine management system , "EMS", acquiring speed information of the vehicle in real-time; an image collecting unit recognizing a pedestrian positioned within a driving lane of the vehicle and detecting information of a relative speed or a distance between the pedestrian and the vehicle , when a speed of the vehicle is greater than or equal to a set speed; and an electronic control unit , "ECU", activating a PDCMS function based on a mapping table using the speed information of the vehicle and information of a motion or a distance of the pedestrian with respect to the vehicle , and controlling a warning unit to inform a driver of a collision of the pedestrian with the vehicle , wherein the PDCMS function includes activating an operation of an active hood, activating an operation of the warning unit , and activating an operation of a brake regardless of whether the driver operates the brake, and the activation of the operation of the warning unit and the activation of the operation of the brake comprise, in order: activating the operation of the warning unit , activating a partial braking of the vehicle , and activating a full braking of the vehicle , wherein the electronic control unit is further configured to determine that the PDCMS function is operated, if an absolute value of the initial speed of the pedestrian at the boundary of a driving lane on which the pedestrian is moving is in a first speed range and the initial speed of the vehicle is in a second speed range at the time of determining whether the PDCMS function is operated, wherein the first speed range has a first minimum speed value and a first maximum speed value, and wherein the second speed range has a second minimum speed value and a second maximum speed value. <EOS>