The invention discloses a stroller auxiliary-wheel device unfoldable along with speed and belongs to the field of articles for children. The stroller auxiliary-wheel device is composed of a chain wheel, first ratchet wheels, a ratchet wheel sleeve, an operating cable, a second ratchet wheel, a flywheel, a spring, a rear shaft, threaded sleeves, nut sleeves, auxiliary wheels, pedals and cranks, wherein the chain wheel and the flywheel are mounted in an alignment manner via a bicycle frame, the cranks are mounted on a shaft of the chain wheel, the pedals are mounted at the other ends of the cranks, the first ratchet wheels are respectively mounted on two sides of the chain wheel, the second ratchet wheel is mounted on one side of the flywheel, the flywheel drives rear wheels to rotate, both the flywheel and the second ratchet wheel are mounted on the rear shaft, the threaded sleeves are mounted on two sides of the flywheel respectively, the spring is mounted at an unthreaded end of one of the threaded sleeves, the outer end of the spring is connected with the ratchet wheel sleeve through the operating cable, the nut sleeves are fittingly mounted on the outer portion of the threaded sleeves, the auxiliary wheels are mounted on supports of the nut sleeves, the nut sleeves are fixed on the rear shaft through slide keys, and the fixed mounting direction of the auxiliary wheels are kept. The stroller auxiliary-wheel device is capable of unfolding the auxiliary wheels along with increase of speed so as to keep a stroller stable.