A novel Sr2MgB2O6 (SMBO) green-emitting phosphor co-doped with Ce3+-Tb3+ was synthesized at 950 °C via solid-state reactions, and the ultra-narrow-band green emission of Tb3+ was significantly enhanced almost 20 times via energy transfer from Ce3+ to Tb3+. It was found to have a broad excitation band (250 to 400 nm), and the full width at half-maximum (FWHM) of the dominant green emission band around 544 nm was only about 10 nm. The electronic band gap of the SMBO matrix was calculated by density functional theory (DFT) to be 4.60 eV, and this was well verified by the diffuse reflection spectra results. Furthermore, the composition-optimized phosphor SMBO:0.05Ce3+,0.05Tb3+ exhibits excellent thermal quenching resistance (75.3% intensity at 423 K) and relatively high external quantum efficiency (EQE = 48.92%). Finally, two white light-emitting diode (WLED) packages were fabricated via combining a 365 nm n-UV chip, the optimal sample and commercial blue and red phosphors to assess the application potential of the phosphors. The test results indicate that the obtained WLEDs-1 fabricated with K2SiF6:Mn4+ has an outstanding color rendering index (Ra = 85.7) and Commission Internationale de L'Eclairage (CIE) coordinates (0.3242, 0.3334). Meanwhile, the color gamut can reach 87% of the National Television Standards Committee (NTSC) CIE 1931 color gamut. WLEDs-2 fabricated with red emitting CaAlSiN3:Eu2+ produced warm white light with color coordinates of (0.3792, 0.3810), a high color rendering index of 82.3, and a low correlated color temperature of 4065 K. These results reveal the broad prospects of this phosphor for LED-based applications.