Steady-state emission and time-correlated single-photon counting (TCSPC) are used to measure the temperature dependence of the proton-transfer rate of wt-GFP in H2O and D2O. As the temperature decreases, the proton-transfer rate from the protonated form slows down. At about 80 K, the rate is about 10-fold slower than the rate at room temperature. At lower temperatures of 70 K down to 13 K (the lowest temperature studied), the rate of proton transfer is almost temperature independent. We explain the temperature dependence of the proton-transfer rate by an intermolecular vibration assisted tunneling mechanism. We attribute the specific intermolecular vibration to the oscillation of two oxygen atoms: the chromophore's phenol ring and the nearby water molecule. The kinetic isotope effect is about 5 and is almost temperature independent.