Abstract: An electrical driving apparatus, which is to mount on a bicycle for driving the bicycle traveling, comprises a driven device is to mount on one side of a back wheel hub of the bicycle. Three secure pieces is to mount the driven device at the interior side to secure the driven device on a disk of the back wheel hub. A motor, which is driven by an electrical power, is to mount on a skeleton of the bicycle for providing a turning power, and a transmission device connects the motor and the driven device for transmitting the turning power of the motor to the driven device to drive the bicycle traveling forward.