A graphene display, and the graphene display's driving method and device are disclosed. The graphene display driving method includes: obtaining the grey-level values of the three primary colors of a pixel to be input; determining the colors and the grey-level values of the two dynamic subpixels and the static subpixel according to the grey-level values of the pixel's three primary colors and a pre-determined correspondence relationship between three primary colors' grey-level values and four primary colors' grey-level values; and applying driving voltages respectively corresponding to the colors and grey-level values of the two dynamic subpixels and the static subpixel to the two dynamic subpixels and the static subpixel. The present disclosure is able to achieve a greater gamut, enhance display quality, and reduce power consumption of the display.