A rolling part steel with which the strength of a rolling part of a cold-worked bearing is improved compared with that of a conventional turned part by controlling the length and number of sulfide inclusions in the steel to an optimal range, when a rolling part steel is prepared so that the maximum length of sulfide inclusions in the steel is 100 .mu.m or less and that a number of sulfide inclusions whose lengths exceed 40 .mu.m is 50 or less per unit area (160 mm.sup.2) , the roughness of its bore surface is improved to have a greater strength. As a result, for example, a thus formed raceway ring has a longer life against fatigue-induced cracks than a turned raceway ring.