With admirable luminescence performance and a cheap price, non-rare-earth-based oxide red phosphors are a potential competitor of rare-earth-doped phosphors for warm white LEDs (WLEDs). Herein, a novel double-perovskite Ba2GdSbO6:Mn4+ phosphor, demonstrating strong red emission ascribed to a spin-forbidden Mn4+:2Eg → 4A2g transition in the region of 620-750 nm, has been synthesized via a solid-state reaction route. The microstructure and luminescence properties are investigated in detail. The concentration quenching mechanism and thermal stability based on thermal quenching characteristics are also discussed. Importantly, Li+, Mg2+, Zn2+, Si4+, Ti4+ and Ge4+ dopants are discovered to be beneficial for enhancing Mn4+ luminescence, and the related mechanisms are comprehensively described. In addition, by combining red-emitting Ba2GdSb0.994O6:0.003Mn4+,0.003Mg2+ with the commercial blue-emitting BaMgAl10O17:Eu2+ and green-emitting Ba3La6(SiO4)6:Eu2+ phosphors in various ratios, a series of WLED devices with a tunable correlated color temperature (CCT) evolving from 6256 to 3486 K and a color rendering index (CRI) increasing from 72.1 to 88.3 are achieved.