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. <EOS>