A method and an apparatus for controlling spindle speed are disclosed. When the speed ranges of respective gear ranges are selected in advance so that speed ranges corresponding to neighboring gear ranges partially overlap one another, and the gear range conforming to the commanded spindle speed is selected for rotating the spindle at the commanded spindle speed, it is determined whether the commanded spindle speed belongs to the currently selected range, no gear change is made if the decision is affirmative, and the gear range to which the newly commanded spindle speed belongs is found if the decision is negative, the gear range being switched to the gear range thus found.