We have calculated evolutionary tracks with alpha-enhanced compositions which cover the entire globular cluster metallicity range and have constructed isochrones which include the effects of microscopic diffusion of helium. The turnoff magnitudes from the isochrones were combined with the theoretical RR Lyrae magnitudes [M(V)(RR)] from Lee to determine the ages of 32 Galactic globular clusters using the magnitude difference between the turnoff and horizontal branch. We find that including the effects of helium diffusion has a negligible effect on the derived ages of globular clusters. Regardless of the inclusion of helium diffusion, we find a significant age spread of 5 Gyr among the globular clusters. The oldest globular clusters studied here are 17 +/- 2 Gyr old.