There is provided an edge shape measurement apparatus and a method of measuring an edge shape capable of accurately measuring the edge shape of a wafer without focusing when scanning with the displacement sensor. The displacement sensor configured to measure the edge shape of the wafer having a plate like shape is provided, and is configured to rotationally be driven taking a predetermined point inside the wafer as a rotational center in a plane which includes the rotational center and is perpendicular to upper and lower surfaces of the wafer while keeping a constant radius with the rotational center, and is configured to measure a distance to a point on a surface of the wafer located on a straight line connecting the rotational center and the displacement sensor by a rotational angle.