A strip rolling mill includes a pair of upper and lower work rolls for rolling a strip, intermediate rolls for supporting each of the paired work rolls, and back-up rolls for supporting each of the intermediate rolls. Each of the work rolls is provided with a tapered portion at one end thereof so that the tapered portions of the work rolls are on opposite sides of roll bodies thereof with respect to roll axis directions. When the material with a constant width is being rolled, axial positions of the work rolls are set at appropriate positions and axial positions of the intermediate rolls are changed to control a thickness distribution in a width direction of the material being rolled. This arrangement significantly improves an edge drop and at the same time minimizes edge drop variations.