The present disclosure provides a compensation circuit, a drive circuit, operating methods of the compensation circuit and the drive circuit, and a display device comprising the drive circuit. The compensation circuit comprises a first compensation module and a second compensation module. The first compensation module generates compensation voltage according to the variation of common electrode voltage, and the second compensation module superposes the compensation voltage inputted by the second input terminal on gamma voltage inputted by the first input terminal, and outputs the superposed gamma voltage. The technical solution above transfers a compensation position from the common electrode voltage to the gamma voltage, and effectively compensates for and inhibits the fluctuation of the common electrode voltage by the compensation voltage superposed on the gamma voltage, thereby avoiding over high temperature of display panels, green tint of displayed images and crosstalk noise.