A hub and axle assembly for a bicycle includes a hub shell rotatably mounted on an axle extending along an axis. A rolling member is interposed between and cooperates with a curved surrounding race portion of a mounting sleeve member secured on the axle and a curved surrounding race member to serve as an anti-friction bearing. A tubular mount member has a tubular engaging portion to engage a left wall segment of the hub shell, and a tubular mount portion extending outwardly of the hub shell to be driven by a uni-directional driving sprocket wheel mechanism. A retaining member is disposed to prevent the mounting sleeve member from moving away from the rolling member.