The present application discloses a graphene display, and a driving method and a driving apparatus for a graphene display, the driving apparatus for a graphene display includes obtaining the grayscale values of the three primary colors of the pixel to be input; determining the color and grayscale values of three dynamic sub-pixels according to the grayscale values of the three primary colors of the pixel and the correspondence relationship of the preset grayscale values of the three primary colors and the grayscale values of the five primary colors; applying the driving voltages to the three dynamic sub-pixels respectively corresponding to the color and grayscale values of three dynamic sub-pixels. By the method described above, the gamut of the display is increased, to increase the display performance of the display and decrease the power consumption of the display.