A method of manufacturing a stabilized fiber bundle is described, which includes subjecting an acrylic fiber bundle aligned, to a heat treatment in an oxidizing atmosphere, with the acrylic fiber bundle being turned around by a guide roller placed on each of both ends outside a hot air heating-type oxidation oven, wherein an air velocity Vm of first hot air sent through a supply nozzle(s) disposed above and/or under a fiber bundle travelled in the oxidation oven, in a substantially horizontal direction to a travelling direction of the fiber bundle, and an air velocity Vf of second hot air flowing in a fiber bundle passing a flow channel in which the fiber bundle is travelled that satisfies expression 1)

0.2≤Vf/Vm≤2.0  1)

to produce a high-quality stabilized fiber bundle and a high-quality carbon fiber bundle at high efficiencies without any process troubles.