The excellent narrow-band emitters, especially the green ones, are regarded as a pivotal research direction for light-emitting diodes (LED) backlights in liquid-crystal displays (LCDs). A nearly single-peak green emission centered at 513 nm with a full width at half maximum of 28 nm is reached in KAl11O17:0.1Eu(2+), 0.15Mn(2+) phosphor via nearly 100% energy transfer (ET) efficiency, and the extended X-ray absorption fine structure analysis elucidates its mechanism, which is that Eu2+ and Mn2+ are constrained to form Eu2+-Mn2+ pairs with a small distance 3.7 angstrom caused by the local environment relaxation inducement. Meanwhile, by creating an unhindered energy flow between Eu2+, Mn2+ and K+/O2- defect levels through ET and multilevel electron trapped and recombination process, the KAO:Eu2+, Mn2+ phosphors perform superb photoluminescence property with a high color purity of 83%, an excellent thermal stability (94%@200 degrees C), and unexceptionable internal and external quantum efficiencies of 91.7% and 66.4%, which all are superior to characteristics of commercial beta-SiAlON:Eu2+ phosphor. Moreover, the white LED fabricated using KAO:Eu2+, Mn2+ to provide green component shows a wide color gamut of 105% National Television System Committee. These results indicate a potential for an application of our material in LCD-LED backlights, and the design of such local relaxation-induced structure provides a significative reference to develop the new narrow-band emitters.