In an elevator apparatus, a car ascends and descends based on a running speed pattern generated by a control panel. Destination floor buttons and landing buttons are connected to an over speed monitoring portion without the intervention of the control panel. The over speed monitoring portion has an over speed setting portion for setting first and second over speeds based on car position information obtained from a car position detector and call registration information obtained from the destination floor buttons and the landing buttons. In the over speed setting portion, a running speed pattern different from the running speed pattern generated by the control panel is independently generated without depending on information from the control panel. The first and second over speeds are set based on the running speed pattern generated by the over speed setting portion.