A pixel circuit is disclosed in the present invention, which includes an OLED, a current-driving unit receiving a signal current on a data line during a programming period to provide a corresponding driving current to the OLED, a first switch coupled between the data line and the current-driving unit and turned on during the programming period to conduct the signal current, and a constant current unit providing a constant current on the data line during a pre-programming period and the programming period. The present invention also discloses an apparatus for driving a display, including a scan-driving circuit, a data-driving circuit, and plural constant current units. A method for driving a pixel having an OLED is also disclosed, which includes the steps of receiving a signal current on a data line during a programming period to provide a corresponding driving current to the OLED, and providing a constant current on the data line during a pre-programming period and the programming period.