A driving method and a driving device of a liquid crystal panel are provided. The driving method includes: creating a position lookup table provided with a first value and a second value respectively indicating a sub-pixel not requiring grayscale compensation and a target sub-pixel requiring grayscale compensation and further for indicating which reference sub-pixel will be used for performing grayscale compensation; creating a compensation lookup table and setting a compensated grayscale value of the target sub-pixel according to a one-to-one relationship between a current grayscale value of the target sub-pixel and a grayscale value of a corresponding reference sub-pixel; and during driving the liquid crystal panel to display, determining the target sub-pixel requiring grayscale compensation and obtaining the corresponding reference sub-pixel according to the position lookup table, obtaining the compensated grayscale value from the compensation lookup table and driving the target sub-pixel to display according to the compensated grayscale value.