Comparing with the conventional CCFL (Cold Cathode Fluorescent Lamp) backlight, three-basic-color LEDs backlight has some advantages such as good color reproduction, long life and lead free etc. Theoretically, the color gamut is determined by x, y coordinates of the three basic colors in CIE chromaticity diagram, and the x, y coordinates of each basic color can derived from the relative spectrum distribution (RSD) of the LED. In this paper, the red, green and blue LEDs' RSD models are established to calculate and analyze the color gamut of a backlight. By simulating those models, the relationships that the color gamut of a LED backlight varies with each color are analyzed, and the optimum combination of three colors is obtained within the given wavelengths ranges. Moreover, the combinations of three colors for the gamut of 115% NTSC and 110% NTSC are plotted in pictures, respectively.