The power driving system includes a motor coupled to reduction gears for driving a set of bevel gears. The bevel gears are coupled to a shaft member having secured thereto a transmission gear to engage with a sprocket wheel to displace a standard chain member. The motor is supplied with DC electricity by a battery which may either be charged by solar cells or alternating current passing through a rectifier supplied by an external power system. Still further, the electric bicycle may have its speed controlled with a user's hand actuated speed controller mechanism.