The invention discloses thin film transistor array substrate and liquid crystal display device thereof, which comprises a plurality of scan lines, a plurality of data lines and a plurality of pixel regions, wherein each pixel region comprises a pixel electrode and a first thin film transistor for controlling the pixel electrode, and each pixel region also comprises a tension alignment electrode, a second thin film transistor for controlling the tension alignment electrode, a first thrust alignment electrode and a second thrust alignment electrode, thereby forming a lateral tension electric field between the tension alignment electrode and the pixel electrode and respectively forming a lateral thrust electric field between the first thrust alignment electrode and the pixel electrode as well as between the second thrust alignment electrode and the pixel electrode when applying a voltage to the thin film transistor array substrate;. By adopting the thin film transistor array substrate, the fast response of liquid crystal molecules can be realized. Besides, a color filter substrate does not need to be provided with a convex structure, thereby improving the contrast ratio, simplifying the manufacturing process and reducing the cost.