In an elevator apparatus, a car is suspended by a suspending means. A braking apparatus applies a braking force to the car by means of the suspending means. An excessive speed detection level that changes in response to car position is set in an excessive speed monitoring portion. The excessive speed monitoring portion makes the braking apparatus perform a braking operation when car speed reaches the excessive speed detection level. An anomalous acceleration detecting mechanism operates a safety device if acceleration that exceeds a preset set value arises in the car.