Phosphor-converted white-light-emitting diodes (pc-WLEDs) rely on combining a near-ultraviolet (n-UV) or blue chip with trichromatic and yellow-emitting phosphors. It is challenging to discover cyan-green-emitting (480-520 nm) phosphors for compensating the spectral gap and producing full-spectrum white light. In this work, we successfully discovered two unprecedented bright cyan-green emitting Rb3RV2O8 (R = Y, Lu) phosphors that gives emission bands centered at 500 nm upon 362 nm n-UV light excitation. Interestingly, the both self-activated compounds exhibit high internal quantum efficiencies (IQEs) of 71% for Rb3RV2O8, and 85% for Rb3RV2O8, respectively. Moreover, controllable emission color can be successfully tuned from cyan-green to orange-red across the warm white light region by design strategy of VO43- -> Eu3+ energy transfer. The thermal quenching of as-prepared phosphors could be effectively mitigated by this design strategy. Finally, the as-fabricated n-UV (lambda(ex) = 370 nm) pumped phosphor-converted (pc) W-LED devices utilizing Rb3RV2O8, (R = Y, Lu) along with commercial phosphors demonstrate well-distributed warm white light with high color-rendering index (CRI) of 91.9 and 93.5, and a low correlated color temperature (CCT) of 5095 and 4946 K. It suggests that the both vanadate phosphors have potential applications in full-spectrum pc-WLEDs.