In this contribution, we propose to combine both narrow-band green (β-sialon:Eu(2+)) and red (K(2)SiF(6):Mn(4+)) phosphors with a blue InGaN chip to achieve white light-emitting diodes (wLEDs) with a large color gamut and a high efficiency for use as the liquid crystal display (LCD) backlighting. β-sialon:Eu(2+), prepared by a gas-pressure sinteing technique, has a peak emission at 535 nm, a full width at half maximum (FWHM) of 54 nm, and an external quantum efficiency of 54.0% under the 450 nm excitation. K(2)SiF(6):Mn(4+) was synthesized by a twe-step co-precipitation methods, and exhibits a sharp line emission spectrum with the most intensified peak at 631 nm, a FWHM of ~3 nm, and an external quantum efficiency of 54.5%. The prepared three-band wLEDs have a high color temperature of 11,184 - 13,769 K (i.e., 7,828 - 8,611 K for LCD displays), and a luminous efficacy of 91 - 96 lm/W, measured under an applied current of 120 mA. The color gamut defined in the CIE 1931 and CIE 1976 color spaces are 85.5 - 85.9% and 94.3 - 96.2% of the NTSC stanadard, respectively. These optical properties are better than those phosphor-cpnverted wLED backlights using wide-band green or red phosphoprs, suggesting that the two narrow-band phosphors investigated are the most suitable luminescent materials for achieving more bright and vivid displays.