We report an effective and rare-earth free light conversion material synthesized via a facile fabrication route, in which organic fluorescent dyes, i.e. Rhodamine B (RhB) and fluorescein isothiocyanate (FITC) are embedded into activated boron nitride (αBN) to form a composite phosphor. The composite phosphor shows highly efficient Förster resonance energy transfer and greatly improved thermal stability, and can emit at broad visible wavelengths of 500-650 nm under the 466 nm blue-light excitation. By packaging of the composite phosphors and a blue light-emitting diode (LED) chip with transparent epoxy resin, white LED with excellent thermal conductivity, current stability and optical performance can be realized, i.e. a thermal conductivity of 0.36 W/mk, a Commission Internationale de 1'Eclairage color coordinates of (0.32, 0.34), and a luminous efficiency of 21.6 lm·W(-1). Our research opens the door toward to the practical long-life organic fluorescent dyes-based white LEDs.