There are provided a driving apparatus of a display panel and a driving method thereof, and a display device. The driving apparatus of the display panel comprises a gate driver circuit (101) configured to input a turn-on signal to each gate line on the display panel at a first moment; and a source driver circuit (102) configured to input a first voltage to each data line on the display panel at a first moment, the first voltage being a common electrode voltage of the display panel. The driving apparatus and the driving method, and the display device are capable of raising the effect of eliminating shutdown image sticking.