The present disclosure provides a Thin Film Transistor Array Substrate and a Liquid Crystal Display apparatus thereof, and relates to the technical field of liquid crystal displaying. The Thin Film Transistor Array Substrate of the present disclosure includes a plurality of gate lines and a plurality of data lines, wherein regions surrounded by the gate lines and the data lines are pixel regions, and wherein a high level common voltage line being used when signal on the data line is at a low level and a low level common voltage lines being used when signal on the data line is at a high level are also arranged in parallel to the gate lines in each of the pixel regions. With the Thin Film Transistor Array Substrate of the present disclosure, the Greenish phenomenon in the existing liquid crystal display apparatus may be effectively solved.