A multi-speed drive hub for a bicycle comprising: a hub shaft connected on a center of a wheel rim of the bicycle, and the hub shaft including a speed-changing transmission arranged on an end of the hub shaft; a speed-changing transmission including at least one drive element arranged on an outer wall of the speed-changing transmission, and the speed-changing transmission including an actuator arranged on an end of the speed-changing transmission and driving multiple force segments of the speed-changing transmission to rotate reciprocately; a speed shifter including a fitting sleeve fitted on the speed-changing transmission, and the fitting sleeve having a third fixing orifice corresponding to the at least one drive element so that the at least one drive element exposes outside the third fixing orifice; a sprocket set including multiple speed cassettes of different diameters, the sprocket set including multiple spacing spaces, each of which is defined any two adjacent speed cassettes; characterized in that the fitting sleeve has multiple ribs extending around an outer wall thereof and has multiple flexible sheets covering the multiple ribs individually; each of the at least one drive elements includes multiple retainers, multiple columns formed from bottoms of the multiple retainers respectively, and multiple force segments arranged on free ends of the multiple retainers and exposing outside the speed-changing transmission; each flexible sheet has a plurality of dented portions and multiple raised portions which are all arranged on an outer wall of each flexible sheet, and each of the plurality of dented portions is defined between any two adjacent raised portions; the sprocket set includes a joining portion formed on a center thereof, a force element secured in the joining portion and connected with the fitting sleeve, and multiple second indentions formed in the force element and retained with the multiple ribs of the speed-changing transmission respectively. a hub shaft connected on a center of a wheel rim of the bicycle, and the hub shaft including a speed-changing transmission arranged on an end of the hub shaft; a speed-changing transmission including at least one drive element arranged on an outer wall of the speed-changing transmission, and the speed-changing transmission including an actuator arranged on an end of the speed-changing transmission and driving multiple force segments of the speed-changing transmission to rotate reciprocately; a speed shifter including a fitting sleeve fitted on the speed-changing transmission, and the fitting sleeve having a third fixing orifice corresponding to the at least one drive element so that the at least one drive element exposes outside the third fixing orifice; a sprocket set including multiple speed cassettes of different diameters, the sprocket set including multiple spacing spaces, each of which is defined any two adjacent speed cassettes; characterized in that the fitting sleeve has multiple ribs extending around an outer wall thereof and has multiple flexible sheets covering the multiple ribs individually; each of the at least one drive elements includes multiple retainers, multiple columns formed from bottoms of the multiple retainers respectively, and multiple force segments arranged on free ends of the multiple retainers and exposing outside the speed-changing transmission; each flexible sheet has a plurality of dented portions and multiple raised portions which are all arranged on an outer wall of each flexible sheet, and each of the plurality of dented portions is defined between any two adjacent raised portions; the sprocket set includes a joining portion formed on a center thereof, a force element secured in the joining portion and connected with the fitting sleeve, and multiple second indentions formed in the force element and retained with the multiple ribs of the speed-changing transmission respectively.