A current driving apparatus and method using a pulse width modulation (PWM) technique to display a desired gray level for passive matrix organic light emitting diode (PMOLED) display applications is disclosed. The current driving circuit includes a memory, a logic and a segment driver. The memory stores a desired gray level, the logic comprises a counter and provides a predetermined bias time, and the segment driver provides a constant current to the PMOLED display based on the desired gray level and the predetermined bias time. The segment driver provides a constant current to the PMOLED display until the counter value reaches the desired gray level, and the counter is first counted zero for the predetermined bias time and then increments by one for every other cycle.