Provided are a driving circuit and a driving method thereof, a touch display panel, and a touch display device. The first input terminal of the delay unit is connected to corresponding previous gate driver, the first output terminal of the delay unit is connected to corresponding subsequent gate driver. The delay unit outputs a starting signal to the subsequent gate driver for enabling it after a predetermined time elapses since the previous gate driver outputs a driving signal. The delay unit achieves shift registering between the previous gate driver and the subsequent gate driver, to form a touch-control time period after the previous gate driver outputs a driving signal and before the subsequent gate driver is enabled, so as to ensure that the touch display panel can also achieve a touch-control function with high precision on the premise of achieving a display function of high resolution.