An organic light emitting display apparatus, capable of removing motion blurring and preventing deterioration in brightness and an increase in power consumption, and a driving method thereof. The organic light emitting display apparatus includes: a plurality of pixels, each pixel including an organic light emitting device (OLED) and a pixel circuit; a data driver applying a data signal to a plurality of data lines connected to the pixels; a scan driver applying a selection signal to a plurality of selection scan lines connected to the pixels; a double speed timing generator doubling a frame frequency and applying a double speed frame signal to the scan driver; and a data signal converter doubling an input data signal, dividing one frame into two frames, applying a first data signal having a level higher than a level of the input data signal in one frame of the two frames, and applying a second data signal having a level lower than the level of the input data signal in the other frame of the two frames.