We present a spectroscopic analysis of the metallicities , ages , and alpha-elements of the globular clusters ( GCs ) in the giant elliptical galaxy ( gE ) NGC 4636 in the Virgo cluster . Line indices of the GCs are measured from the integrated spectra obtained with Faint Object Camera and Spectrograph ( FOCAS ) on the Subaru 8.2 m Telescope . We derive [ Fe/H ] values of 59 GCs based on the Brodie & Huchra method , and [ Z/H ] , age , and [ \alpha /Fe ] values of 33 GCs from the comparison of the Lick line indices with single stellar population models . The metallicity distribution of NGC 4636 GCs shows a hint of a bimodality with two peaks at \textrm { [ Fe / H ] } = -1.23 ( \sigma = 0.32 ) and -0.35 ( \sigma = 0.19 ) . The age spread is large from 2 Gyr to 15 Gyr and the fraction of young GCs with age < 5 Gyr is about 27 % . The [ \alpha /Fe ] of the GCs shows a broad distribution with a mean value [ \alpha /Fe ] \approx 0.14 dex . The dependence of these chemical properties on the galactocentric radius is weak . We also derive the metallicities , ages , and [ \alpha /Fe ] values for the GCs in other nearby gEs ( M87 , M49 , M60 , NGC 5128 , NGC 1399 , and NGC 1407 ) from the line index data in the literature using the same methods as used for NGC 4636 GCs . The metallicity distribution of GCs in the combined sample of seven gEs including NGC 4636 is found to be bimodal , supported by the KMM test with a significance level of > 99.9 % . All these gEs harbor some young GCs with ages less than 5 Gyr . The mean age of the metal-rich GCs ( [ Fe/H ] > -0.9 ) is about 3 Gyr younger than that of the metal-poor GCs . The mean value of [ \alpha /Fe ] of the gE GCs is smaller than that of the Milky Way GCs . We discuss these results in the context of GC formation in gEs .