An apparatus for extruding a weather strip having first and second function portions and a connecting portion interconnecting these function portions is disclosed. The connecting portion varies in width according to a longitudinal position along the weather strip. Included in the apparatus is a head, a main die plate which is mated with a front side of the head and which has a first opening for extruding rubber therethrough to form a first function portion, such as a mounting portion, and part of the connecting portion, a fixed die plate connected to the main die plate, and a movable die disposed in the fixed die plate. The movable die has a second opening for extruding rubber therethrough to form a second function portion, such as a sealing portion, and part of the connecting portion and is slidably received in a reception portion in the fixed die plate. A discharge rate of the rubber for forming the connecting portion is adjustable in accordance with the sliding movement of the movable die. Burrs on the resulting weather strip are therefore avoided. Also, sacrificial portions of the rubber are not generated. The second opening in the movable die is formed into a required special configuration, and by moving the movable die, the width of the connecting portion can be easily varied while maintaining the shape of the seal portion.