A method and apparatus for controlling current of an organic light emitting diode (OLED) display device, which is able to accurately estimate the amount of current according to an input image and control current to converge upon target current disclosed. The apparatus includes a current controller for estimating a total current value using a peak luminance corresponding to an average picture level of input data and a histogram analysis result of the input data, comparing an estimated total current value and a target value to generate a luminance control gain, feeding the luminance control gain back and repeatedly performing an operation for estimating the total current value and generating the luminance control gain to determine a final luminance control gain, and applying the final luminance control gain to the peak luminance to determine a final peak luminance, a gamma voltage generator, and a data driver.