The present invention provides a composite roll for cold rolling capable of rolling a cold-rolled steel strip having little edge drop, a cold-rolled stainless steel strip or a bright finish steel strip having excellent surface brightness or a silicon steel strip excellent in magnetic properties without causing breakage of roll, which is a roll in which a sleeve is fitted at a surrounding of a shaft portion with the shaft portion as a central axis and its fabrication method, in which the sleeve is constituted by previously integrating a plurality of pieces of mold members divided by a face intersecting with the central axis of the roll. Further, this is a fit roll in which a sleeve member of an outermost layer is made of WC—Co series hard alloys having Young's modulus of 35000 kgf/mm or more and Co content of 12-50 weight % and is provided with a wall thickness of 3% or more of roll radius and a ratio L/D of a length L of a barrel of the sleeve to a diameter D of the roll falls in a range of 2-10. Further, when there are one layer or more of intermediate layers between the outermost layer of the sleeve and the shaft core, the intermediate layers are arranged such that Young's modulus of the layer on the outer side is larger than Young's modulus of the layer on the inner side.