To prevent the inner face of a tube to be rolled from generating a crack by making a Q value and T. Red a specific value so that tensile stress generated at a Pilger rolling time is crossed to metal fibers by using a base tube is which the metal fibers have an angle for the tube axial direction.

A stock billet 1 is heated to a prescribed temp., is pierced and rolled by a piercer roll 2 and is made to a hollow base tube 3 in which metal fibers have an angle for the tube axial directionn. The rolling is conducted under a Q value of ≥0.4 and T.Red of ≤80% while satisfying the absolute value of the Q value=thickness working rate/outer shape working rate=1n(t1/t0)/1n(dm1/dm0) and the formula of the T.Red=area reduction rate (%)=(1-dm1×t1/dm0×t0)×100, wherein t0=base tube thickness, t1=product thickness, d0=base tube outer diameter, dm0=d0-t0 and dm1=d1-t1.