In a tandem mill system, at least one first type rolling mill is arranged in the upstream side and at least one second type rolling mill is arranged in the downstream side. The first type rolling mill is of the so-called work roll crossing mill in which a pair of work rolls are inclined with respect to a pair of back-up rolls supporting the work rolls and simultaneously crossed each other in a horizontal plane to control transverse thickness distribution of a strip. The second type rolling mill is of the so-called HC mill which controls the strip crown and shape by a combination of axial movement of intermediate rolls and work roll bending. Such an arrangement makes it possible to increase a capability of controlling the strip crown and shape, particularly, a capability of correcting the quarter buckle, and eliminate a fear of causing scratches on the strip and roll surfaces, with the result of improved production efficiency. Plural lines of lubricant supply device are also provided to stop supply of a lubricant immediately before biting of the strip into the work roll crossing mill and start the supply again after the biting. A system of lubricating the work roll crossing mill is thereby improved.