The invention discloses a grid electrode driving circuit and a driving method thereof and a display device. The circuit comprises at least two scanning modules which are connected with a same clock signal, and each scanning module comprises at least one stage of a shifting register unit, wherein the scanning module is provided with an input end used for enabling the shifting register units in the scanning module to output grid electrode starting voltage stage by stage under driving of the clock signal from the moment that the effective electric level is received, and the scanning module is further provided with a reset end used for enabling the last-stage shifting register unit in the scanning module to stop grid electrode starting voltage output when the effective electric level is received; the scanning modules are sequentially arranged from front to back, and the reset end of the previous scanning module in every two adjacent scanning modules and the input end of the next scanning modules in the two adjacent scanning modules are connected with a starting moment reset signal line and an end moment starting signal line respectively, wherein the starting moment reset signal line and the end moment starting signal line correspond to a same touch scanning time period. Accordingly, the stability of the output potential of the first row of grid electrodes after touch scanning is finished can be kept.