A thin film transistor array substrate, a driving method therefore, and a liquid crystal display are disclosed. The thin film transistor array substrate includes at least a sub-pixel region formed by a gate line and a data line intersected with each other, wherein, each sub-pixel comprises a first transistor (21) of which the gate is connected with a gate line and the drain is connected with a data line and a first storage capacitor (23) of which one end is connected with the source of the first transistor (21) and the other end is connected with an output of a reference voltage, the sub-pixel further comprises a second storage capacitor (24) and a second transistor (25), wherein one end of the second storage capacitor (24) is connected with the source of the first transistor (21), and the other end of the second storage capacitor (24) is connected with the drain of the second transistor (25); the source of the second transistor (25) is connected with the output of the reference voltage, and the gate of the second transistor (25) is connected with an output of an Enable signal. Since a second storage capacitor (24) is additionally added to each sub-pixel in the thin film transistor array substrate, the capacitance of the storage capacitors during static display is increased, the voltage conversion frequency during static display is deceased, and the system power consumption is decreased.