A kneading apparatus includes a barrel having a cylindrical chamber; a screw assembly rotating in the chamber so that a material to be kneaded is extruded in the axial direction by the rotation, the screw assembly including a screw section having helical blades and a kneading blade section in order to allow the material to flow into the clearance between the inner wall of the chamber and the kneading blade section, and to apply shearing forces to the material; a metering feeder for feeding the material at a substantially constant volumetric or gravimetric rate into the chamber; an injecting device for injecting a heat-removing medium into the chamber; and a discharging device for separating the heat-removing medium from the material and discharging the heat-removing medium from the chamber. A kneading method using the kneading apparatus is also disclosed.