Blue-green dual-emitting phosphors Ca₃Lu(GaO)₃(BO₃)₄:Ce³⁺,Tb³⁺ (CLGB:Ce³⁺,Tb³⁺) were synthesized via a traditional solid-state reaction method. The phase of the phosphors was characterized by X-ray diffraction and the luminescence properties were investigated using the excitation and emission spectra, decay curves, temperature-dependent emission spectra, CIE chromaticity coordinates, and the internal quantum efficiency. Under 345 nm UV light excitation, Ce³⁺ singly doped CLGB phosphors presented intense blue light in the 350–550 nm wavelength region with a maximum peak at 400 nm. In sharp contrast, CLGB:Ce³⁺,Tb³⁺ phosphors showed both the blue and green emission wavelengths of Ce³⁺ and Tb³⁺ ions, respectively. The overall emission colors can be tuned from blue (0.164, 0.042) to green (0.331, 0.485) via increasing the concentration of Tb³⁺ ions, due to the energy transfer (ET) from Ce³⁺ ions to Tb³⁺ ions. The optimal doping concentration of Tb³⁺ ions in CLGB:Ce³⁺,Tb³⁺ phosphors was found to be 40 mol%. The mechanism of the ET from the Ce³⁺ to Tb³⁺ ions was demonstrated to be electric quadrupole–quadrupole interaction. The CLGB:0.04Ce³⁺,0.40Tb³⁺ sample possessed a high IQE of 54.2% and excellent thermal stability with an activation energy of 0.3142 eV when excited at 345 nm. The integrated emission intensity of CLGB:0.04Ce³⁺,0.40Tb³⁺ at 423 K was found to be about 74% of that at 303 K. Finally, under 300 mA driven current, the fabricated prototype white light-emitting diode showed CIE chromaticity coordinates of (0.3996, 0.3856) and high color rending index of 81.2. Considering all the above characteristics, the obtained CLGB:Ce³⁺,Tb³⁺ phosphors can be a type of multicolor emitting phosphor for application in white light-emitting diodes.