An accelerating system for improving the running speed of a bicycle including: a main hub housing, a hub bush engaged with the main hub housing and having a sun gear, a gear cover having latches and having fixed shafts for rotatably supporting planetary gears in a meshing engagement with the sun gear, a gear housing having a ring gear with a gear-type engaging portion positioned on the hub shaft such that the planetary gears engage with the ring gear, a locker threadedly engaged with the gear-type engaging member, a hollow cylindrical auxiliary hub housing having an inner stage portion for receiving an outer periphery surface of the gear housing, and an auxiliary hub housing cover having a gear latch portion for engaging with the latches of the gear cover such that the auxiliary hub housing cover only rotates in one direction.