A ball bearing assembly for a bicycle comprises a outer race, a ball cage, settled in the outer race, a cap, having a center hole and a ring portion extended axially from the periphery of the center hole, an inner race, with the inner surface thereof closely surrounding the outer surface of the ring portion, and a packing ring which is in an annular shape and having an annular flange around the bottom outer edge so that when the cap is put over the outer race to make the ball cage press upon the ball cage, the packing ring can be inserted into the center hole of the cap, and the flange is retained around the bottom of the ball cage. The disclosed ball bearing assembly is characterized by improved assembling accuracy and automatic center adjusting function.