Efficient blue-light-excitable broadband cyan-emitting phosphors may yield full-visible-spectrum white light-emitting diodes (WLEDs) with ultrahigh color rendering (Ra > 95). However, this requires closing the "cyan gap" in the 480-520 nm region of the visible spectrum, which is challenging. Herein, a well-performed cyan-emitting garnet phosphor Ca2LuAlGa2Si2O12:Ce3+ (CLAGSO:Ce3+) is reported. Under 430 nm excitation, the optimal CLAGSO:5%Ce3+ compound exhibits a broadband cyan emission (peak, 496 nm; bandwidth, 102 nm) with a high internal quantum efficiency of 85.6% and an excellent thermal resistance performance (69.1% at 423 K). Importantly, this as-prepared cyan-emitting phosphor provides sufficient cyan emission and enables filling the well-known so-called "cyan gap" between the blue LED chip and the commercial Y3Al5O12:Ce3+ (YAG:Ce3+) yellow phosphor. Impressively, a WLED device fabricated with the optimal CLAGSO:5%Ce3+ sample shows a low correlated color temperature (4053 K) and an ultrahigh color rendering index (Ra = 96.6), as well as an excellent luminous efficacy (74.09 lm W-1). These results highlight the importance of blue-excited broadband cyan-emitting phosphors in closing the cyan gap and enabling human-centric full-visible-spectrum warm WLED devices for high-quality solid-state lighting.