The present invention provides an LDO regulator having a greatly improved overshoot characteristic through the use of an output voltage based feedback loop. More specifically, in the invention, one or more resistors in the divider network in a conventional LDO regulator is replaced with a variable resistor. By varying the resistance of the variable resistor as a function of the output voltage of the LDO regulator, the closed-loop gain of the LDO amplifier may be modulated in such a way as to reduce overshoot in the output voltage of the LDO regulator. In particular, the targeted final output voltage value may be arbitrarily lowered for a predetermined period of time, so that the LDO regulator output may rapidly reach a steady state voltage that is very close to the final desired regulating value without exceeding the final desired regulating value during regulator startup.