The current commercial white light-emitting diodes (LEDs) are generally based on the combination of blue LED chips and Y3Al5O12:Ce3+ yellow phosphors. However, because of the lack of red component, such white LED devices exhibit cool white-light emissions with low color rendering index (Ra < 75, R9 < 0). Therefore, it is urgent to discover new blue-light-excitable yellow-emitting phosphors with enhanced red emissions for fabricating high color-quality white LEDs. In the present work, we demonstrate a novel broadband yellow-emitting CaGd2HfScAl3O12:Ce3+ garnet phosphor for blue-light-excited white LEDs with improved color rendering index. The as-prepared CaGd2HfScAl3O12:Ce3+ garnet phosphor possesses a cubic structure with Ia3¯d space group, and the unit cell parameters of the representative CaGd2HfScAl3O12:2%Ce3+ phosphor are a = b = c = 12.450 Å, α = β = γ = 90°, and V = 1,929.59(4) Å3. Impressively, we find that the CaGd2HfScAl3O12:Ce3+ garnet phosphor shows an intense absorption band in the 300–500 nm wavelength range with a maximum at 452 nm owing to the 4f→5d transition of Ce3+ ions. On 452 nm excitation, the optimal CaGd2HfScAl3O12:2%Ce3+ sample exhibits a broad asymmetric yellow emission band in the wavelength range of 470–750 nm with peak at 564 nm and full width at half maximum of 151 nm. The Commission Internationale de l’Eclairage chromaticity coordinates and internal quantum efficiency of the CaGd2HfScAl3O12:2%Ce3+ sample are (0.4485, 0.5157) and 30.4%, respectively. Finally, a white LED device is fabricated by combing a 450 nm blue LED chip with commercial Y3Al5O12:Ce3+ yellow-emitting phosphor, which generates white light with low color rendering index (CRI; Ra = 74.7, R9 = −12.7) and high correlated color temperature (CCT = 6,554 K) under the 60 mA driving current. In sharp contrast, another white LED device, which is made by coating our as-prepared CaGd2HfScAl3O12:2%Ce3+ yellow-emitting phosphors onto the surface of a 450 nm blue LED chip, produces white-light emission with high CRI value (Ra = 84.5, R9 = 26.3) and relatively low CCT of 5,649 K. This work reveals that the newly discovered broadband yellow-emitting CaGd2HfScAl3O12:Ce3+ phosphors can serve as a potential color converter in high-color-quality phosphor-converted white LEDs.