An electronic device may have a display such as a liquid crystal display. The display may have an array of pixels that display images to a user. Backlight structures may provide the array of pixels with backlight illumination at a backlight illumination level. The backlight structures may have a light source with an array of light-emitting diodes and photoluminescent material that is pumped by pump light from the light-emitting diodes. The backlight illumination may experience color variations as a function of the backlight illumination level. Circuitry in the electronic device may be used to implement a backlight level color compensator. The backlight level color compensator may apply color correction factors to the image data of the displayed images to compensate for variations in color of the image data due to variations in backlight illumination level and operating temperature.