Abstract: A power driving device for a bicycle has a planetary gear assembly mounted with a driving axle shaft, including a housing fixed to the bicycle frame with a side wall rotatably mounting the driving axle shaft and a flange wall projecting laterally from the side wall which contains the planetary gear assembly and has a ring gear fixed thereto, a pinion gear carrier fixed to the driving axle shaft for rotation together therewith upon application of a driving force to the pedals, and a sun gear fixedly connected to a driving sprocket wheel for transmitting power from the pedals to the rear wheel of the bicycle. The planetary gear assembly can provide a power changing ratio in the range of about 3.5, so that the driving sprocket wheel can have a number of teeth substantially less than the number of teeth on a conventional sprocket wheel yet, when multiplied by the power changing ratio of the planetary gear assembly, is equivalent to more than double that of the conventional sprocket wheel.