Abstract: An intravenous catheter set includes a needle 1, having a proximal end 5 and a distal end 3 and a catheter 2, in which the needle 1 is detachably inserted in such a manner that the sharpened end 3 of the needle 1 extends from a front end of the catheter 2, which has a front end equal to or slightly smaller in outer diameter than the distal end 3 which forms a sharpened end, and which has its base end gradually reduced in diameter rearward to form a reduced-diameter portion 4 with a tapered surface 4a. Portion 4 is followed by the proximal end 5 which gradually increases in diameter rearwardly to form a tapered portion 5 corresponding in shape to a front end 7 of the catheter 2, to minimize the resistance of a blood vessel's wall against the catheter 2 in piercing the vessel's wall with the needle and to substantially prevent a front end of the catheter 23 from rolling back or tearing.