High light-quality and low color temperature are two crucial factors for a comfortable healthy illumination. Phosphor-converted white light-emitting diodes (LEDs) could be readily realized by combining near-UV (380–420 nm) LED chips with tri-color phosphors, and thus near-UV-excitable inorganic phosphors with efficient visible luminescence are highly demanded for fabricating high-performance near-UV-pumped white LEDs. Herein, we demonstrated a novel highly efficient green-emitting phosphor based on Ce 3+ /Tb 3+ ions co-activated Ca 2 GdHf 2 Al 3 O 12 (abbreviated as: CGHAO) garnet compound, which enabled the realization of ultra-high color rendering warm-white LEDs. Notably, the CGHAO:Ce 3+ ,Tb 3+ phosphors could be efficiently excited by near-UV light around 408 nm and exhibited intense green emissions around 543 nm with high internal quantum efficiency of 82.7% and external quantum efficiency of 60.6%. The energy transfer from Ce 3+ to Tb 3+ ions was studied in detail, and the composition of CGHAO:Ce 3+ ,Tb 3+ phosphors was optimized. Utilizing the optimal CGHAO:0.04Ce 3+ ,0.4Tb 3+ green phosphor as color converter, a prototype near-UV-pumped white LED device was fabricated, and upon 120 mA driving current it demonstrated bright warm-white light with excellent CIE chromaticity coordinates of (0.391, 0.360), low correlated color temperature of 3575 K, ultra-high color rendering index (Ra = 94.4, R12 = 89.0, and R9 = 80.6) and good luminous efficacy of 27.40 lm·W −1 . This work offers a new strategy for designing efficient LED phosphors for high-color-quality solid-state lighting.