An organic light emitting diode (OLED) display and a method for driving the same, which can display an image with more uniform luminance is disclosed. In one aspect, the OLED display includes a plurality of pixels arranged in a matrix of a plurality of rows and a plurality of columns; a data driver supplying second data signals corresponding to a second data obtained by converting a first data, in response to first data signals corresponding to the first data or a data control signal; and a compensator converting output currents output from the pixels, corresponding to the first data signals into a output voltages, and supplying, to the data driver, the data control signal for converting the first data into the second data, corresponding to the output voltages and the first data based on the output voltages and the first data.