We present a library of synthetic spectra characterized by -2.5<=[Z/Z_{sun}]<=+0.5, 4.5<=logg<=1.0, and T_eff<=7500K computed at the same {lambda}/{Delta}{lambda}=20000 resolving power of the observed spectra given in Paper I (Munari, 1999, Cat. ) for 131 standard stars mapping the MKK spectral classification system. This range of parameters includes the majority of the galactic stars expected to dominate the GAIA target population, i.e. F-G-K-M type stars with metallicity ranging from that of the galactic globular clusters to Population I objects. Extension to T_eff_>7500K will be given later on in this series. The 254 synthetic spectra presented here are based on Kurucz's codes and line data and have been computed over a more extended wavelength interval (7650-8750{AA}) than that currently baselined for implementation on GAIA, i.e. the 8500-8750{AA}. This last range is dominated by the near-IR Ca II triplet and the head of the Paschen series. The more extended wavelength range allows us to investigate the behaviour of other strong near-IR spectral features (severely contaminated by telluric absorptions in ground-based observed spectra) as the K I doublet (7664, 7699{AA}), the Na I doublet (8183, 8194{AA}) and the lines of Fe I multiplet N.60 at 8327 and 8388{AA}. The synthetic spectra support our previous conclusions about the superior performance of the Paschen/Ca II 8500-8750{AA} region in meeting the GAIA requirements when compared to other near-IR intervals of similar {Delta}{lambda}=250{AA}.