A catheter introducer valve assembly of a catheter introducer leading to a blood vessel of a patient for positioning at least one catheter tube through the catheter introducer and its sheath to a blood vessel of a patient. The valve assembly unit has first and second valves, the first valve being for preventing or minimizing the flow of blood from the valve assembly unit when the catheter tube is absent from the catheter introducer and the second valve being for preventing or minimizing the flow of blood when the catheter tube is present in the catheter introducer. The first valve, which is made of a flexible, resilient material, is shaped as a disk having a valve slit, such a duckbill valve, positioned diametrically across the passage of the valve assembly body. The rim surface of the valve disk has a slightly smaller diameter than the diameter of the positioning area of the inner surface of the valve assembly body where the valve disk is located so that a cylindrical space is formed therebetween. A pair of opposed holding bosses connected to the disk rim are located in the cylindrical space transverse to the direction of the valve slit. Pressure against the valve disk by any flow of blood is resisted by the pressure of the holding bosses against the inner surface of the positioning area so that the lips of the valve are kept pressed together to shut off or minimize the flow of blood. Also, the holding bosses help to close the lips of the valve during the withdrawal procedure of the catheter tube from the introducer assembly.