We obtained spectra of some 140 globular clusters (GCs) associated with the Virgo central cD galaxy M87 with the Subaru/FOCAS MOS mode. The fundamental properties of GCs such as age, metallicity, and {alpha}-element abundance are investigated by using simple stellar population models. It is confirmed that the majority of M87 GCs are as old as, more metal-rich than, and more enhanced in {alpha}-elements than the Milky Way GCs. Our high-quality, homogeneous data set enables us to test the theoretical prediction of inflected color-metallicity relations (CMRs). The nonlinear-CMR hypothesis entails an alternative explanation for the widely observed GC color bimodality, in which even a unimodal metallicity spread yields a bimodal color distribution by virtue of nonlinear metallicity-to-color conversion. The newly derived CMRs of old, high-signal-to-noise-ratio GCs in M87 (the V-I CMR of 83 GCs and the M-T2 CMR of 78 GCs) corroborate the presence of the significant inflection. Furthermore, from a combined catalog with the previous study on M87 GC spectroscopy, we find that a total of 185 old GCs exhibit a broad, unimodal metallicity distribution. The results corroborate the nonlinear-CMR interpretation of the GC color bimodality, shedding further light on theories of galaxy formation.