the present invention discloses a method for driving thin film transistor liquid crystal display and the storage medium for storing computer program representative of the method thereof . the method utilizes a timing controller to send polarity control signals to a plurality of source drivers in a tft - lcd panel for changing the polarity distribution of the liquid crystal molecules in the panel . the method is characterized by dynamically changing the positions of polarity inversion for alleviating the problem of undercharging under high resolution and high frequency conditions ; utilizing both polar and reverse polar driving signals for solving the problem of color shift in “ checker board ” checking signals ; and providing a mechanism for mending the problem of undercharging of the first horizontal line .