The invention discloses a shift register and a driving method thereof, and a gate driving circuit. The shift register comprises a pull-up sub-circuit which is used for providing a signal of a forwardscanning signal end for a pull-up node under the control of a first input end, and is also used for providing a signal of a reverse scanning signal end for the pull-up node under the control of a second input end; an output sub-circuit, used for providing a signal of a clock signal end for the signal output end under the control of the pull-up node; a pull-down sub-circuit, used for providing a signal of a first power supply end for the pull-down node under the control of the first control end or the second control end, and providing a signal of a second power supply end for the pull-down nodeunder the control of the first input end, the second input end and the pull-up node; and a noise reduction sub-circuit, used for providing signals of the second power supply end for the pull-up nodeand the signal output end under the control of the pull-down node. According to the technical scheme provided by the invention, the working stability, the use reliability and the display effect of thedisplay panel are improved.