An apparatus for operating a pedestrian detection and collision mitigation system (PDCMS) of a vehicle, comprising: a front detection sensor configured to detect a pedestrian in a driving lane of the vehicle and a distance and a relative speed between the pedestrian and the vehicle; a vehicle sensor configured to detect a speed of the vehicle; a controller configured to execute the PDCMS function based on information detected by the front detection sensor and the vehicle sensor; and a warning unit operated by the controller to provide a notification to a driver regarding a collision of the pedestrian with the vehicle, wherein the front detection sensor includes: an image input unit configured to acquire an image of an area at a front of the vehicle; an ROI setting unit configured to set a region of interest that corresponds to a size of an object in the image; a candidate extraction unit configured to extract a pedestrian candidate based on a movement of the object in the set ROI; and a pedestrian determination unit configured to compare the extracted pedestrian candidate with a posture of a sample pedestrian in a database to identify whether the extracted pedestrian candidate corresponds to the pedestrian, characterized in that the controller is further configured to determine that the PDCMS function is operated, if an absolute value of an initial speed of the pedestrian at a boundary of the driving lane in which the pedestrian is moving is in a first speed range and an initial speed of the vehicle is in a second speed range at the time of determining whether the PDCMS function is operated, the first speed range has a first minimum speed value and a first maximum speed value, and the second speed range has a second minimum speed value and a second maximum speed value. a front detection sensor configured to detect a pedestrian in a driving lane of the vehicle and a distance and a relative speed between the pedestrian and the vehicle; a vehicle sensor configured to detect a speed of the vehicle; a controller configured to execute the PDCMS function based on information detected by the front detection sensor and the vehicle sensor; and a warning unit operated by the controller to provide a notification to a driver regarding a collision of the pedestrian with the vehicle, wherein the front detection sensor includes: an image input unit configured to acquire an image of an area at a front of the vehicle; an ROI setting unit configured to set a region of interest that corresponds to a size of an object in the image; a candidate extraction unit configured to extract a pedestrian candidate based on a movement of the object in the set ROI; and a pedestrian determination unit configured to compare the extracted pedestrian candidate with a posture of a sample pedestrian in a database to identify whether the extracted pedestrian candidate corresponds to the pedestrian, characterized in that an image input unit configured to acquire an image of an area at a front of the vehicle; an ROI setting unit configured to set a region of interest that corresponds to a size of an object in the image; a candidate extraction unit configured to extract a pedestrian candidate based on a movement of the object in the set ROI; and a pedestrian determination unit configured to compare the extracted pedestrian candidate with a posture of a sample pedestrian in a database to identify whether the extracted pedestrian candidate corresponds to the pedestrian, characterized in that the controller is further configured to determine that the PDCMS function is operated, if an absolute value of an initial speed of the pedestrian at a boundary of the driving lane in which the pedestrian is moving is in a first speed range and an initial speed of the vehicle is in a second speed range at the time of determining whether the PDCMS function is operated, the first speed range has a first minimum speed value and a first maximum speed value, and the second speed range has a second minimum speed value and a second maximum speed value.