there are provided an organic light emitting diode display driving apparatus and a driving method thereof , in which the oled display panel driving apparatus of a passive matrix type is configured such that its scan driving circuit has 3 - state output , and the cathode lines , selected when the scan driving circuit performs a scan operation , maintain grounding , and after data - applied oled emits light , are switched in a high voltage , and execute a refresh operation to initialize the pixel charges , and with the high impedance state maintained , non - selective common cathode lines turn into a high impedance state so as to remove the parasitic capacitance elements , and reduce the capacitance element functioning as the load of the data driving circuit connected to the oled anode lines , and without the use of precharge method of maintaining the anode lines above a predetermined voltage quickly by using a voltage source , and applying data by using a current source , the anode lines can be charged within a short time just by necessary current for the lightening of the oled so as to reduce the power consumption of the data driving circuit , and increase the operation speed .