Here, Tb3+ ions are incorporated into Cs2Ag0.6Na0.4InCl6:Bi double perovskite microcrystals via a re-crystallization method. Tb3+ ions doping not only makes the white light spectrum adjustable, but also maintains the high photoluminescence quantum yield (PLQY). The optimal value of PLQY is 95%. These are comparable to the current highest values. Noteworthy is that, intrinsic emission of Tb3+ ions is attributed to the effective energy transfer from the trapped exciton state of the double perovskite host to Tb3+ ions. Finally, mixing 30% Tb3+ alloyed Cs2Ag0.6Na0.4InCl6:Bi and Cs2NaInCl6:10%Sb phosphors, a series of double-perovskite-based white light-emitting diodes (WLEDs) are prepared. The color coordinates of the best WLEDs are (0.34, 0.32), the lumen efficiency is 42 lm/W, and the color rendering index is 94.3. It is worth mentioning here that there is no blue light loss caused by energy reabsorption between the two phosphors, because the excitation wavelengths of the two phosphors are concentrated in the ultraviolet band. This work provides a new strategy for preparing high-performance WLED.