PURPOSE: To provide a device which is also applicable to a small H-shape steel having relatively low web height in an eccentric sleeve edging rolling device of web eccentric type.

CONSTITUTION: This device is provided with an edging rolls 7 which are provided on the right and left of driving shafts 8, eccentric sleeves 10 which are fit so that position around the driving shaft is adjustable between both those edging rolls 7 and web constraining ring rolls 12 which are freely rotatably fit to the outer peripheral surface of the sleeve 10, the width W of the outside surfaces of the rolls 12 is formed larger than the half width FS of the flanges of shapes of rolled stock and also the web constraining ring rolls are made into an integrated type in the direction of the driving shafts. And the outside diamters of the eccentric sleeves 10 are formed larger than the outside diameters of the edging rolls 7 and eccentric sleeve positioning devices 13 with which the position of eccentric sleeve 10 around the driving shaft is adjusted are provided in side edge parts on the side of the edging rolls 7 of the eccentric sleeves 10. The H-shape steel with low web height is produced by reducing roll surface where is exposed to the rolled stock with use of this device.