A single-piece woven fiber structure for fabricating an axisymmetric part of varying diameter made out of composite material, the fiber structure having a portion of frustoconical shape with a large diameter and a small diameter, the ratio between the large diameter and the small diameter being not less than 2. The fiber structure is formed by winding layers of warp and weft yarns that are woven on a mandrel having a profile that is defined as a function of the profile of the part to be fabricated with warp yarn take-up. For each layer of yarns, the weft yarns are angularly distributed on a single diameter in a zone of the large diameter of the portion of frustoconical shape and on at least two different diameters in a zone of the small diameter of the portion of frustoconical shape in order to form at least two superposed plies of weft yarns.