The purpose of this paper is to make clear the cause of movement of velocity-change-point in the roller drafting zone, because the movement is closely connected with the sliver irregularity delivered. A fundamental means to control the sliver irregularity is proposed.By using of the theory of velocity-change-point developed by Foster, it is shown that the position of velocity-change-point in the drafting zone is determined by the frictional force between floating fibres and roller gripped fibres. In this case, the characteristics of sliver density in the zone have very important effects on the frictional force. When the variation of sliver density becomes large, the sliver irregularity increases. The fundamental means to control the sliver irregularity is to reduce the variation of sliver density in roller drafting.