We present spectroscopy for globular clusters (GCs) in the elliptical galaxy NGC 4365, obtained with the LRIS spectrograph on the Keck I telescope. Previous studies have shown that the optical color distribution of GCs in NGC 4365 lacks the bimodal structure that is common in globular cluster systems, showing only a single broad peak. Measurements of Balmer line indices (Hbeta, Hgamma and Hdelta) on the GC spectra support recent suggestions by Puzia et al., based on optical and near-infrared photometry, that some of the clusters in NGC 4365 are intermediate-age (2-5 Gyrs) and metal-rich (-0.4<[Z/H]<0) rather than old (~10-15 Gyrs) and metal-poor. We also find some genuinely metal-poor, old clusters, suggesting that the ages and metallicities of the two populations conspire to produce the single broad distribution observed in optical colors.