a terminal slowdown apparatus for an elevator which reads in outputs given by contacting a car with terminal detectors placed depending upon a terminal floor to operate a terminal slowdown signal which is reduced depending upon the distance to the terminal floor and to output the lower signal between the normal speed command signal and the terminal slowdown signal , including a first processor which outputs an acceleration command signal increasing from the start of the car at an acceleration lower than an acceleration of the car given in the start of the car during the saturation fault of the normal speed command signal ; a terminal detector which is placed at the point wherein the acceleration command signal is equal to the terminal slowdown command signal generated at the position reaching to the normal slowdown starting position in the rated speed running of the car ; a second processor which operates the slowdown command reducing depending upon the distance from the terminal floor to the position for operating the terminal detector ; and a third processor which compares the output of the first processor with the output of the second processor to output the lower output as the terminal slowdown command signal .