To provide a tube stock of excellent dimensional accuracy by keeping a taper plug in the full-float condition with one pair of four-roll stands as large diameter roll and with the other pair as small diameter rolls to dispense with the positional adjustment of the plug.

In a tube rolling mill in which hole type stands of four-roll type are continuously arranged, a large diameter roll bites a tube stock 4 and moves it in the axial direction. A small diameter roll 2 follows the tube stock 4 and is turned to prevent a tapered plug 3 from being pulled inside the tube stock 4 after the thickness is reduced. The tapered plug 3 is arranged on the inner surface of the tube stock 4 so that the diameter Dp of a parallel finished part meets the condition of the formula I. The small diameter roll 2 is of non- driven roll, and has the diameter of the groove bottom so that the biting angle θs of the tube stock 4 is (2β+2)-25°. The tube stock 4 is cold rolled by displacing the center of rotation of the large diameter roll pair to the roll-advancing direction from the center of rotation of the small diameter roll 2 pair within the range to meet the condition of the formula II.