A multi-speed drive hub for a bicycle contains: a hub shaft, a speed-changing transmission, a speed shifter, and a sprocket set. The hub shaft is connected on a center of a wheel rim of the bicycle and includes a speed-changing transmission. The speed-changing transmission includes at least one drive element and an actuator for driving multiple force segments of the speed-changing transmission to rotate reciprocately. The speed shifter includes a fitting sleeve which has a third fixing orifice corresponding to the at least one drive element. The sprocket set includes multiple speed cassettes of different diameters and includes multiple spacing spaces, each of which is defined any two adjacent speed cassettes. The fitting sleeve has multiple ribs and multiple flexible sheets. Each drive elements includes multiple retainers, multiple columns, and multiple force segments.