Distribution of fluorescence resonance energy transfer (FRET) efficiency between the two ends of a Lennard-Jones polymer chain both at equilibrium and during folding and unfolding has been calculated, for the first time, by Brownian dynamics simulations. The distribution of FRET efficiency becomes bimodal during folding of the extended state subsequent to a temperature quench, with the width of the distribution for the extended state broader than that for the folded state. The reverse process of unfolding subsequent to a upward temperature jump shows different characteristics. The distributions show significant viscosity dependence which can be tested against experiments.