The invention provides a shift register, as well as a drive method, a grid drive device, and a display device thereof. The shift register comprises a precharge unit, a pull-up control unit, a pull-up unit, a pull-down control unit and a pull-down unit, wherein the precharge unit is connected with an initial signal input terminal, a first clock signal input terminal, a control node, and a low level output terminal of a drive power supply; the pull-up control unit is connected with the control node, a pull-up node, the first clock signal input terminal, and a high level output terminal and the low level output terminal of the drive power supply; the pull-down control unit is connected with the control node, a pull-down node, and the high level output terminal and the low level output terminal of the drive power supply; the pull-up unit is connected with the pull-up node and an output terminal; the pull-down unit is connected with the pull-down node, the output terminal and the low level output terminal of the drive power supply respectively; and a first clock signal and a second clock signal are opposite in phase. The utility model solves the problems of unstable output waveforms and high noise.