A kneading screw is disclosed which comprises a screw body, the screw body comprising a feed section and a kneading section, the feed section comprising screw segments for feeding a to-be-kneaded material to a downstream side and the kneading section comprising kneading segments for kneading the material. The screw body is provided within the kneading section with a multi-stage portion which gradually changes axially in rotating outside diameter. It is preferable that the multi-stage portion be constituted by kneading segments of plural kneading discs different in rotating outside diameter. With such a construction, it is possible to avoid stress concentration on an axial part of the kneading screw and thereby prevent breaking of a spline shaft and abnormal wear of kneading flights.