Disclosed is a bicycle which is a means of short-distance movement favored by men and women of all ages. The present invention is an application of a bicycle having a motor-generator disclosed in Korean Patent Application No. 2009-035298 that the applicant of the present invention filed. Namely, a motor-generator is mounted on a side of the rear wheel of the bicycle, and a control box and a battery are mounted under the main pipe of the bicycle, and a change-over switch and a change speed switch are mounted on the handle of the bicycle. The present invention makes it possible to charge quickly and effectively via a motor-generator that is operated by the bicycle driving force on a downhill or level ground, and with charging made, the rotary force of the motor-generator is conveyed to the rear wheel to generate electric power, so that electromotive force is produced and stored by itself, and the driving force of the bicycle can be obtained by using the stored electric power. Therefore, it is possible to use the bicycle easily and conveniently for a long time, and it has an effect of much reduced leg fatigue even in the case of moving a long distance.