A driving substrate and a driving method thereof and a liquid crystal display device. The driving substrate includes driving electrodes and a control chip. A time period of a frame is divided into at least a first time period, a second time period and a third time period. The control chip configured to: in the first time period, apply a first group of data voltages to respective driving electrodes to control corresponding pixels to be equivalent to liquid crystal lenses having first curvatures; in the second time period, apply a second group of data voltages to the respective driving electrodes to control the corresponding pixels to be equivalent to liquid crystal lenses having second curvatures; and in the third time period, apply a third group of data voltages to the respective driving electrodes to control the corresponding pixels to be equivalent to liquid crystal lenses having third curvatures.