A drive circuit, a drive method of the drive circuit and a display device are provided. The drive circuit includes a signal output module, a first level signal output end; and a plurality of switch modules. The signal output module includes N output ends for outputting a gate drive signal step by step to N scan lines. The switch modules each correspond to one of the scan lines. A control end of the i-th switch module is electrically connected with the i−1th scan line. A first connecting end is electrically connected with the corresponding i-th scan line. A second connecting end is electrically connected with the first level signal output end. Wherein, N is a positive integer, and i is a positive integer greater or less or equal to N.