To provide a spiral motion system imparting correct roll grinding.

In a continuous spiral motion system for rolling a strip 6 extended within a rolling mill stand which is composed of at least a set of upper and lower work rolls 4, 5, backup rolls corresponding to respective work rolls 4, 5, a means for continuously transferring the work rolls 4, 5 in the axial direction during the strip 6 is rolled, and a means for imparting a spiral rolling motion of the work rolls 4, 5 to a rotational motion of the work rolls 4, 5 with respect to the rolled strip 6, respective work rolls 4, 5 are provided with a substantially longer length than the width of the strip 6 to be rolled.