A series of novel dysprosium(III) (Dy3+)-doped yellow-emitting double-perovskite A2BB'O6 (A = calcium(II) (Ca2+), B = lanthanum(III) (La3+), gadolinium(III) (Gd3+), and indium(III) (In3+); B′ = antimony(V) (Sb5+), tantalum(V) (Ta5+), and niobium(V) (Nb5+)) phosphors were synthesized. The ion substitution in B and B′ sites in the double-perovskite structure significantly affected its crystal structures and photoluminescence properties such as excitation spectrum, emission spectrum, thermal stability, color purity, luminescence dynamic, and quantum yield. Interestingly, the beneficial thermal stability of all the obtained samples (> 62% at 423 K with respect to the initial value at 303 K) implied their potential for solid-state lighting application. Among them, the Ca2LaTaO6:Dy3+ exhibited the best heat resistance (> 83% at 423 K) while the Ca2GdNbO6:Dy3+ had the highest internal quantum yield up to 35.17%. Furthermore, the possible mechanisms for the changes in luminescent properties relying on their chemical compositions were studied accordingly. Eventually, some fabricated light-emitting diode devices based on the obtained samples were tested for their application in warm solid-state lighting.