Cool stars, such as M giants, can only be analyzed in the near-infrared (NIR) regime due to the ubiquitous titanium oxide features in optical spectra of stars with Teff<4000K. In dust-obscured regions, the inner bulge and Galactic center region, the intrinsically bright M giants observed in the NIR are an optimal option for studying stellar abundances and the chemical evolution of stellar populations. Because of the uncertainties in photometric methods, a method for determining the stellar parameters for M giants from the NIR spectra themselves is needed. We develop a method for determining the stellar parameters for M giants from the NIR spectra. We validate the method by deriving the stellar parameters for nearby well-studied M giants with spectra from the spectral library of the Immersion GRating INfrared Spectrograph (IGRINS). We demonstrate the accuracy and precision of our method by determining the stellar parameters and alpha-element trends versus metallicity for solar neighborhood M giants. We carried out new observations of 44 M giant stars with IGRINS mounted on the Gemini South telescope. We also obtained the full H and K band IGRINS spectra of six nearby well-studied M giants at a spectral resolving power of R=45000 from the IGRINS spectral library. We used the tool called spectroscopy made easy in combination with one-dimensional (1D) model atmospheres in a radiative and convective scheme (MARCS) stellar atmosphere models to model the synthetic spectrum that fits the observed spectrum best. The effective temperatures that we derive from our new method (tested for 3400<=Teff<=4000K here) agree excellently with those of the six nearby well-studied M giants, which indicates that the accuracy is indeed high. For the 43 solar neighborhood M giants, our Teff, logg, [Fe/H], microturbulence, [C/Fe], [N/Fe], and [O/Fe] agree with APOGEE with mean differences and a scatter (our method - APOGEE) of -67+/-33K, -0.31+/-0.15dex, 0.02+/-0.05dex, 0.22+/-0.13km/s, -0.05+/-0.06dex, 0.06+/-0.06dex, and 0.02+/-0.09dex, respectively. Furthermore, the tight offset with a small dispersion compared to the APOGEE Teff indicates a high precision in our derived temperatures and those derived from the APOGEE pipeline. The typical uncertainties in the stellar parameters are found to be +/-100K in Teff, +/-0.2dex in logg, +/-0.1dex in [Fe/H], and +/-0.1km/s in microturbulence. The alpha-element trends versus metallicity for Mg, Si, Ca, and Ti are consistent with the APOGEE DR17 trends for the same stars and with the GILD optical trends. We also find a clear enhancement in the abundances for thick-disk stars.