A new oxynitride, Ba3Si6O12N2, has been synthesized. The crystal structure has been successfully determined by close collaboration between experiment and first-principles calculation. This compound doped with Eu exhibits intense green photoluminescence with high color purity under near-ultraviolet to blue light excitation; in particular, it has much less thermal quenching than (Ba,Sr,Eu)2SiO4. Thus (Ba,Eu)3Si6O12N2 appears promising green phosphor for white LED backlight for display. The atomic/electronic structure is discussed in comparison with Ba3Si6O9N4, which could not become efficient phosphor by doping Eu due to strong thermal quenching at room temperature.