The present disclosure discloses a method and apparatus for driving an organic light emitting display and an organic light emitting display. In embodiments of the present disclosure, when a respective current signal input from each power signal line to a respective pixel circuit exceeds a preset current threshold, voltage attenuation on the power signal line can be compensated by applying a compensation signal to the respective pixel circuit connected to the power signal line, thereby improving uniformity of display images of the organic light emitting display and enhancing quality of display images of the organic light emitting display.