An apparatus for activating a pedestrian detection and collision mitigation system (PDCMS) of a vehicle, the apparatus comprising: a front detection sensor detecting a presence of a pedestrian on a driving lane of the vehicle, gaze information of the pedestrian, and a distance and a relative speed between the pedestrian and the vehicle; a vehicle sensor detecting at least one of a speed, an acceleration, a steering angle, a steering angular velocity, and a pressure of a master cylinder of the vehicle; an electronic control unit activating a PDCMS function based on information detected by the front detection sensor and the vehicle sensor; and a warning unit operating to inform a driver of a collision of the pedestrian with the vehicle by a control of the electronic control unit, wherein the PDCMS function includes activating an operation of the warning unit and activating an operation of a brake regardless of whether the driver operates the brake, wherein the activation of the operation of the warning unit and the activation of the operation of the brake are performed in order of the activation of the operation of the warning unit, a partial braking of the vehicle, and 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 and the initial speed of the vehicle are in an area in which the PDCMS function is essentially operated at the time of determining whether the PDCMS function is operated, wherein the electronic control unit is further configured to control an operating time (t 1, t 2) of the PDCMS function based on the gaze information of the pedestrian, and wherein the gaze information of the pedestrian is determined based on a horizontal length of the entire face of the pedestrian, a horizontal length from a left face contour to a left eye of the pedestrian, a horizontal length from a right face contour to a right eye of the pedestrian, and a horizontal length between the left eye and the right eye of the pedestrian. a front detection sensor detecting a presence of a pedestrian on a driving lane of the vehicle, gaze information of the pedestrian, and a distance and a relative speed between the pedestrian and the vehicle; a vehicle sensor detecting at least one of a speed, an acceleration, a steering angle, a steering angular velocity, and a pressure of a master cylinder of the vehicle; an electronic control unit activating a PDCMS function based on information detected by the front detection sensor and the vehicle sensor; and a warning unit operating to inform a driver of a collision of the pedestrian with the vehicle by a control of the electronic control unit, wherein the PDCMS function includes activating an operation of the warning unit and activating an operation of a brake regardless of whether the driver operates the brake, wherein the activation of the operation of the warning unit and the activation of the operation of the brake are performed in order of the activation of the operation of the warning unit, a partial braking of the vehicle, and 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 and the initial speed of the vehicle are in an area in which the PDCMS function is essentially operated at the time of determining whether the PDCMS function is operated, wherein the electronic control unit is further configured to control an operating time (t 1, t 2) of the PDCMS function based on the gaze information of the pedestrian, and wherein the gaze information of the pedestrian is determined based on a horizontal length of the entire face of the pedestrian, a horizontal length from a left face contour to a left eye of the pedestrian, a horizontal length from a right face contour to a right eye of the pedestrian, and a horizontal length between the left eye and the right eye of the pedestrian.