PURPOSE: To improve the dimensional accuracy in the tip part of a rolled stock by controlling the speed of each rolling mill in terms of feedforward when rolling is started.

CONSTITUTION: In a speed controller for a continuous rolling mill, a correcting device 8 with which an initial set speed of each rolling mill 1 on the downstream side from a 2nd rolling mill 1 is corrected by ΔVi+1=α.{(1+Fi)/(1-Gi+1)}.ΔV1 based on a difference ΔL between the detected amount of loop by a loop detecting means 7 and the objective amount of loop when rolling is started is connected to each driving device 2. Where, ΔV2={1/(1- G2)}.ΔL/ΔT, subscript: the number of rolling mill and i≥2, Fi: the forward slip of steel sheet at a i-th rolling mill, Gi+1: the backward slip at a (i+1)th rolling mill, ΔT: loop detecting time, α: correction factor.