  Adopting the SPECTRUM package, we have synthesized a set of 2,890
Near-InfraRed (NIR) synthetic spectra with a resolution and wavelength sampling
similar to the SDSS and the forthcoming LAMOST spectra. During the synthesis,
we have applied the `New grids of ATLAS9 Model Atmosphere' to provide a grid of
local thermodynamic equilibrium (LTE) model atmospheres. This synthetic stellar
library is composed of 1,350 solor scaled abundance (SSA) and 1,530 non-solar
scaled abundance (NSSA) spectra, grounding on which we have defined a new set
of NIR CaII triplet indices and an index CaT as the sum of the three. Then,
these defined indices have been automatically measured on the synthetic spectra
and calibrated with the indices computed on the observational spectra from the
INDO-U.S. stellar library. In order to check the effect of alpha-element
enhancement on the so-defined CaII indices, we have compared indices measured
on the SSA spectra with those on the NSSA ones at the same terns of stellar
parameters (Teff, log g, [Fe/H]), and luckily, little influences of
alpha-element enhancement has been found. Furthermore, comparisons of synthetic
indices with the observational ones from the INDO-U.S. spectra, the SDSS-DR7,
and DR8 spectroscopic survey have been presented respectively for dwarfs and
giants in detail. Finally, a new synthetic library of NIR CaII indices has been
founded for deeper studies on the NIR waveband of stellar spectra, and is
particularly appropriate for the SDSS and the forthcoming LAMOST stellar
spectra. Later on, we have regressed the strength of the CaT index as a
function of stellar parameters for both dwarfs and giants after a series of
experimental investigations into relations of the indices with stellar
parameters. Ultimately, a supplemental experimentation has been carried out to
show that spectral noises do have effects on our set of NIR CaII indices.
