We used an inhomogeneous excited-state proton-transfer kinetics model to explain the origin of the non-exponential time-resolved emission of the A-band of wt-green fluorescence protein. The calculated fit is rather good for both H2O and D2O samples in a wide temperature range of 80-229 K. We attribute the inhomogeneous kinetics to the distance dependence of the excited-state proton-transfer rate between the proton donor (the hydroxyl group of the chromophore) and the oxygen of a nearby water molecule.