The invention discloses a thin film transistor drive circuit and a drive method thereof and a liquid crystal display device. The thin film transistor drive circuit includes a plurality of scan lines, a scan signal output port configured to sequentially apply a scan signal to each of the scan lines, and a plurality of logic circuits. Each of the logic circuits is connected with one of the scan lines and a control signal line. The logic circuits are added to a drive circuit, and an input control signal corresponding to a truth table of the logic circuit is input for a preset duration by using a logic relationship of the logic circuit, so that an output control signal output to a scan line can be obtained to improve a scan signal on the scan line, to improve a delay distortion at the time of being turned off.