We present a spectroscopic study of the globular clusters (GCs) in the giant elliptical galaxy (gE) NGC 4636 in the Virgo cluster. Line indices of GCs in NGC 4636 are measured from the integrated spectra obtained with Faint Object Camera and Spectrograph (FOCAS) on the Subaru Telescope. We derive the [Fe/H] of the GCs in NGC 4636 using Brodie & Huchra (1990) method. The [Z/H], age, and alpha-element of the GCs are obtained from the comparison of the Lick line indices with the SSP model grid. We investigate the distribution and radial variation of the metallicity, age, and alpha-element of NGC 4636 GCs. The metallicity distribution of NGC 4636 GCs shows a bimodality. The chemical properties of these GCs show little radial variation. These results will be discussed with regard to the formation and evolution of NGC 4636.