To reduce the cost of equipment in a rolling line for steel bars and wire rods.

In this method, a stock for steel bars and wire rods is successively rolled and its area is reduced with 2-roll mill train 100 in which 2-roll mills are continuously arranged in multistage at 90° phase and the finish rolling of the stock is executed with two 4-roll mills S1, S2 which are arranged in the fixed positions of the rearmost stage of the 2-roll mill train 100. When the diameter of a product is small, all stand No.1-No.l6 of the 2-roll mill train and 4-roll mills S1, S2 are operated at high speed and, when the diameter of the product is large, arbitrary stands No.9-No.16 of the poststage of the 2-roll mill train are stopped and the stands No.1-No.8 of the stage preceding the stopped stands and the 4-roll mills S1, S2 are operated at low speed. To change the speed of the 4-roll mills S1, S2, a gear speed-changers are put between rolls and roll driving motors and these changers are switched between the high-speed position and the low-speed position with spline type engaging mechanisms.