Fluorescence resonance energy transfer between CdSe (480 nm) quantum dots (donor) and fluorescein 27 (acceptor) is studied using steady state and time-resolved fluorescence measurements at room temperature in toluene based solutions. Decrease in the fluorescence intensity of QD donor and increase in the dye emission intensity with increasing concentration of acceptor dye and a significant reduction of the fluorescence lifetime of the QDs in the presence of acceptor are noted. The results indicate the occurrence of efficient FRET in this system and also a clear dependence of FRET efficiency on the spectral overlap between the QD emission spectrum and the dye absorption spectrum.