A portable drug delivery device for delivering a drug in liquid or fluid form at a constant and self-regulated rate to a patient comprises a syringe having spring loaded piston reciprocal in a cylinder having a reverse taper to pressurize the drug to be dispensed. The reverse taper on the cylinder results in decreasing friction on the piston as the piston moves in the cylinder during a dispensing cycle, and is designed to compensate for the decreasing force exerted on the piston by the expanding spring. A length of tubing connected to the syringe conveys the drug to a needle or other device for administering the drug to a patient, and a restrictor in the length of tubing impedes flow of the drug to achieve a desired flow rate. The restrictor may be sized to achieve any desired flow rate, and in a preferred form of the invention comprises a laser-burned hole in a fitting attached to the outlet end of the length of tubing.