A continuous kneading apparatus including: a stationary portion having an internal space where matter is conveyed; a rotary disc member and a screw member which are configured to convey the matter in the internal space; a drive shaft member to which the rotary disc member and the screw member are fixed; and a cooling medium passage through which a cooling medium passes, wherein the cooling medium passage is provided for the screw member which is placed upstream of the rotary disc member with respect to the conveyance direction of the matter, wherein the cooling medium passing in the cooling medium passage is lower in temperature than the matter passing in the internal space, and wherein the matter passes in the internal space while provided with shear force by rotation of the drive shaft member and thus continuously kneaded, and while cooled by the cooling medium.