Motivated by recent experiments on photon statistics from individual dye pairs planted on biomolecules and coupled by fluorescence resonance energy transfer (FRET), we show here that the FRET dynamics can be modeled by Gaussian random processes with colored noise. Using Monte Carlo numerical simulations, the photon intensity correlations from the FRET pairs are calculated, and are turned out to be very close to those observed in experiment. The proposed stochastic description of FRET is consistent with existing theories for microscopic dynamics of the biomolecule that carries the FRET coupled dye pairs.