An apparatus for measuring surface roughness of a rail, comprising: a traveling platform configured to move in a longitudinal direction along a rail; a cantilever beam having a fixed end fixed to the traveling platform and a movable end extending in the longitudinal direction; a contact member provided at the movable end of the cantilever beam to make contact with a top surface of the rail; an acceleration sensor provided at the movable end of the cantilever beam to measure vertical acceleration of the contact member generated by irregularities of a top surface of the rail; and a displacement sensor configured to contact the top surface of the rail to measure vertical displacement caused by the irregularities of the top surface of the rail while the apparatus is running along the rail, wherein the cantilever beam is located to face the top surface of the rail, the contact member and the displacement sensor move along the rail in contact with the top surface of the rail, and surface roughness of the rail is measured from an acceleration signal measured by the acceleration sensor and a vertical displacement measurement signal measured by the displacement sensor, wherein a plurality of displacement sensors is arranged in a row to configure a displacement sensor set, and the displacement sensor set is rotatably provided at the traveling platform so that the displacement sensors are arranged with an angle with respect to a longitudinal direction of the center of the rail, wherein a horizontally installed plate is provided at the traveling platform, wherein a coupling hole and a rotation slot are formed through the horizontally installed plate, wherein one of the plurality of displacement sensors of the displacement sensor set, arranged in a row, corresponds to a rotation center displacement sensor which is coupled through the coupling hole of the horizontally installed plate, and wherein in the displacement sensor set, a displacement sensor adjacent to the rotation center displacement sensor is inserted through the rotation slot so that the displacement sensor set is coupled to be rotatable with respect to the horizontally installed plate. a traveling platform configured to move in a longitudinal direction along a rail; a cantilever beam having a fixed end fixed to the traveling platform and a movable end extending in the longitudinal direction; a contact member provided at the movable end of the cantilever beam to make contact with a top surface of the rail; an acceleration sensor provided at the movable end of the cantilever beam to measure vertical acceleration of the contact member generated by irregularities of a top surface of the rail; and a displacement sensor configured to contact the top surface of the rail to measure vertical displacement caused by the irregularities of the top surface of the rail while the apparatus is running along the rail, wherein the cantilever beam is located to face the top surface of the rail, the contact member and the displacement sensor move along the rail in contact with the top surface of the rail, and surface roughness of the rail is measured from an acceleration signal measured by the acceleration sensor and a vertical displacement measurement signal measured by the displacement sensor, wherein a plurality of displacement sensors is arranged in a row to configure a displacement sensor set, and the displacement sensor set is rotatably provided at the traveling platform so that the displacement sensors are arranged with an angle with respect to a longitudinal direction of the center of the rail, wherein a horizontally installed plate is provided at the traveling platform, wherein a coupling hole and a rotation slot are formed through the horizontally installed plate, wherein one of the plurality of displacement sensors of the displacement sensor set, arranged in a row, corresponds to a rotation center displacement sensor which is coupled through the coupling hole of the horizontally installed plate, and wherein in the displacement sensor set, a displacement sensor adjacent to the rotation center displacement sensor is inserted through the rotation slot so that the displacement sensor set is coupled to be rotatable with respect to the horizontally installed plate.