We derive a strong bound on the axion-photon coupling g(a gamma) from the analysis of a sample of 39 Galactic Globular Clusters. As recognized long ago, the R parameter, i.e., the number ratio of stars in horizontal over red giant branch of old stellar clusters, would be reduced by the axion production from photon conversions occurring in stellar cores. In this regard, we have compared the measured R with state-of-the-art stellar models obtained under different assumptions for g(a gamma). We show that the estimated value of g(a gamma) substantially depends on the adopted He mass fraction Y, an effect often neglected in previous investigations. Taking as a benchmark for our study the most recent determinations of the He abundance in H II regions with O/H in the same range of the Galactic Globular Clusters, we obtain an upper bound g(a gamma) < 0.66 x 10(-10) GeV-1 at 95\% confidence level. This result significantly improves the constraints from previous analyses and is currently the strongest limit on the axion-photon coupling in a wide mass range.