An OLED display with a current stabilizing device employs a voltage boosting and current stabilizing device which is coupled between the driving-voltage line of the data driver and the data-power-supply wires to produce an output voltage higher than the driving voltage by boosting the driving voltage of the data driver, and then to maintain the current of the OLEDs at a constant level by performing current limiting, so that the problem of the current-ununiformity caused uneven luminance of the conventional OLED display can be solved, and the possibility that the luminance of the OLED panel will decay in a short period of time is reduce.