The invention provides an array substrate gate drive circuit and a driving method thereof, and a display device. The array substrate gate drive circuit comprises at least one shift register group; and each shift register group consists of a plurality of shift registers arranged in cascaded connection. The plurality of shift registers includes a first shift register, a second shift register connected behind the first shift register, and a third shift register connected behind the second shift register. The third shift register is provided with an initial terminal connected to the output terminal of the first shift register.