Disclosed are a gate driving circuit and a driving method thereof, and a display device using the driving circuit. In the gate driving circuit, a Qn node in a nth-stage circuit is precharged when a Qn−1 node output signal in a previous-stage driving circuit and a Qn+1 node output signal in a next-stage driving circuit are both at high levels, and thus stability of a Gn output end in the nth-stage circuit can be greatly improved. Meanwhile, a first transistor and a second transistor are connected in series, and a third transistor and a fourth transistor are connected in series.