The Sloan Digital Sky Survey-III (SDSS-III) Apache Point Observatory Galactic Evolution Experiment (APOGEE) has obtained high-resolution (R~22,500), high signal-to-noise ratio (S/N) spectra in the H-band (~1.5–1.7 um) for about 146,000 stars in the Milky Way galaxy. We have computed spectral libraries with effective temperature (Teff) ranging from 3500 to 8000 K for the automated chemical analysis of the survey data. The libraries, used to derive stellar parameters and abundances from the APOGEE spectra in the SDSS-III data release 12 (DR12), are based on ATLAS9 model atmospheres and the ASSeT spectral synthesis code. We present a second set of libraries based on MARCS model atmospheres and the spectral synthesis code Turbospectrum. The ATLAS9/ASSeT (Teff=3500–8000 K) and MARCS/Turbospectrum (Teff=3500–5500 K) grids cover a wide range of metallicity (-2.5 < [M/H] < +0.5 dex), surface gravity (0 < log g < 5 dex), microturbulence (0.5 < v_micro < 8 km/s), carbon (-1 < [C/M] < +1 dex), nitrogen (-1 < [N/M] < +1 dex), and alpha-element (-1 < [alpha/M] < +1 dex) variations, having thus seven dimensions. We compare the ATLAS9/ASSeT and MARCS/Turbospectrum libraries and apply both of them to the analysis of the observed H-band spectra of the Sun and the K2 giant Arcturus, as well as to a selected sample of well-known giant stars observed at very high resolution. The new APOGEE libraries are publicly available and can be employed for chemical studies in the H-band using other high-resolution spectrographs.